In C/C++ what's the simplest way to reverse the order of bits in a byte?

Question

While there are multiple ways to reverse bit order in a byte, I'm curious as to what is the "simplest" for a developer to implement. And by reversing I mean:

1110 -> 0111
0010 -> 0100

This is similar to, but not a duplicate of this PHP question.

This is similar to, but not a duplicate of this C question. This question is asking for the easiest method to implement by a developer. The "Best Algorithm" is concerned with memory and cpu performance.

Answer 1

This should work:

unsigned char reverse(unsigned char b) {
   b = (b & 0xF0) >> 4 | (b & 0x0F) << 4;
   b = (b & 0xCC) >> 2 | (b & 0x33) << 2;
   b = (b & 0xAA) >> 1 | (b & 0x55) << 1;
   return b;
}

First the left four bits are swapped with the right four bits. Then all adjacent pairs are swapped and then all adjacent single bits. This results in a reversed order.

Answer 2

I think a lookup table has to be one of the simplest methods. However, you don't need a full lookup table.

//Index 1==0b0001 => 0b1000
//Index 7==0b0111 => 0b1110
//etc
static unsigned char lookup[16] = {
0x0, 0x8, 0x4, 0xc, 0x2, 0xa, 0x6, 0xe,
0x1, 0x9, 0x5, 0xd, 0x3, 0xb, 0x7, 0xf, };

uint8_t reverse(uint8_t n) {
   // Reverse the top and bottom nibble then swap them.
   return (lookup[n&0b1111] << 4) | lookup[n>>4];
}

// Detailed breakdown of the math
//  + lookup reverse of bottom nibble
//  |       + grab bottom nibble
//  |       |        + move bottom result into top nibble
//  |       |        |     + combine the bottom and top results 
//  |       |        |     | + lookup reverse of top nibble
//  |       |        |     | |       + grab top nibble
//  V       V        V     V V       V
// (lookup[n&0b1111] << 4) | lookup[n>>4]

This fairly simple to code and verify visually.
Ultimately this might even be faster than a full table. The bit arith is cheap and the table easily fits on a cache line.

Answer 3

If you are talking about a single byte, a table-lookup is probably the best bet, unless for some reason you don't have 256 bytes available.

Answer 4

Since nobody posted a complete table lookup solution, here is mine:

unsigned char reverse_byte(unsigned char x)
{
    static const unsigned char table[] = {
        0x00, 0x80, 0x40, 0xc0, 0x20, 0xa0, 0x60, 0xe0,
        0x10, 0x90, 0x50, 0xd0, 0x30, 0xb0, 0x70, 0xf0,
        0x08, 0x88, 0x48, 0xc8, 0x28, 0xa8, 0x68, 0xe8,
        0x18, 0x98, 0x58, 0xd8, 0x38, 0xb8, 0x78, 0xf8,
        0x04, 0x84, 0x44, 0xc4, 0x24, 0xa4, 0x64, 0xe4,
        0x14, 0x94, 0x54, 0xd4, 0x34, 0xb4, 0x74, 0xf4,
        0x0c, 0x8c, 0x4c, 0xcc, 0x2c, 0xac, 0x6c, 0xec,
        0x1c, 0x9c, 0x5c, 0xdc, 0x3c, 0xbc, 0x7c, 0xfc,
        0x02, 0x82, 0x42, 0xc2, 0x22, 0xa2, 0x62, 0xe2,
        0x12, 0x92, 0x52, 0xd2, 0x32, 0xb2, 0x72, 0xf2,
        0x0a, 0x8a, 0x4a, 0xca, 0x2a, 0xaa, 0x6a, 0xea,
        0x1a, 0x9a, 0x5a, 0xda, 0x3a, 0xba, 0x7a, 0xfa,
        0x06, 0x86, 0x46, 0xc6, 0x26, 0xa6, 0x66, 0xe6,
        0x16, 0x96, 0x56, 0xd6, 0x36, 0xb6, 0x76, 0xf6,
        0x0e, 0x8e, 0x4e, 0xce, 0x2e, 0xae, 0x6e, 0xee,
        0x1e, 0x9e, 0x5e, 0xde, 0x3e, 0xbe, 0x7e, 0xfe,
        0x01, 0x81, 0x41, 0xc1, 0x21, 0xa1, 0x61, 0xe1,
        0x11, 0x91, 0x51, 0xd1, 0x31, 0xb1, 0x71, 0xf1,
        0x09, 0x89, 0x49, 0xc9, 0x29, 0xa9, 0x69, 0xe9,
        0x19, 0x99, 0x59, 0xd9, 0x39, 0xb9, 0x79, 0xf9,
        0x05, 0x85, 0x45, 0xc5, 0x25, 0xa5, 0x65, 0xe5,
        0x15, 0x95, 0x55, 0xd5, 0x35, 0xb5, 0x75, 0xf5,
        0x0d, 0x8d, 0x4d, 0xcd, 0x2d, 0xad, 0x6d, 0xed,
        0x1d, 0x9d, 0x5d, 0xdd, 0x3d, 0xbd, 0x7d, 0xfd,
        0x03, 0x83, 0x43, 0xc3, 0x23, 0xa3, 0x63, 0xe3,
        0x13, 0x93, 0x53, 0xd3, 0x33, 0xb3, 0x73, 0xf3,
        0x0b, 0x8b, 0x4b, 0xcb, 0x2b, 0xab, 0x6b, 0xeb,
        0x1b, 0x9b, 0x5b, 0xdb, 0x3b, 0xbb, 0x7b, 0xfb,
        0x07, 0x87, 0x47, 0xc7, 0x27, 0xa7, 0x67, 0xe7,
        0x17, 0x97, 0x57, 0xd7, 0x37, 0xb7, 0x77, 0xf7,
        0x0f, 0x8f, 0x4f, 0xcf, 0x2f, 0xaf, 0x6f, 0xef,
        0x1f, 0x9f, 0x5f, 0xdf, 0x3f, 0xbf, 0x7f, 0xff,
    };
    return table[x];
}

Answer 5

See the bit twiddling hacks for many solutions. Copypasting from there is obviously simple to implement. =)

For example (on a 32-bit CPU):

uint8_t b = byte_to_reverse;
b = ((b * 0x0802LU & 0x22110LU) | (b * 0x8020LU & 0x88440LU)) * 0x10101LU >> 16;

If by “simple to implement” one means something that can be done without a reference in an exam or job interview, then the safest bet is probably the inefficient copying of bits one by one into another variable in reverse order (already shown in other answers).

Answer 6

template <typename T>
T reverse(T n, size_t b = sizeof(T) * CHAR_BIT)
{
    assert(b <= std::numeric_limits<T>::digits);

    T rv = 0;

    for (size_t i = 0; i < b; ++i, n >>= 1) {
        rv = (rv << 1) | (n & 0x01);
    }

    return rv;
}

EDIT:

Converted it to a template with the optional bitcount

Answer 7

There are many ways to reverse bits depending on what you mean the "simplest way".

---

Reverse by Rotation

Probably the most logical, consists in rotating the byte while applying a mask on the first bit (n & 1):

unsigned char reverse_bits(unsigned char b)
{
    unsigned char   r = 0;
    unsigned        byte_len = 8;

    while (byte_len--) {
        r = (r << 1) | (b & 1);
        b >>= 1;
    }
    return r;
}

1. As the length of an unsigner char is 1 byte, which is equal to 8 bits, it means we will scan each bit while (byte_len--)

2. We first check if b as a bit on the extreme right with (b & 1); if so we set bit 1 on r with | and move it just 1 bit to the left by multiplying r by 2 with (r << 1)

3. Then we divide our unsigned char b by 2 with b >>=1 to erase the bit located at the extreme right of variable b. As a reminder, b >>= 1; is equivalent to b /= 2;

---

Reverse in One Line

This solution is attributed to Rich Schroeppel in the Programming Hacks section

unsigned char reverse_bits3(unsigned char b)
{
    return (b * 0x0202020202ULL & 0x010884422010ULL) % 0x3ff;
}

1. The multiply operation (b * 0x0202020202ULL) creates five separate copies of the 8-bit byte pattern to fan-out into a 64-bit value.

2. The AND operation (& 0x010884422010ULL) selects the bits that are in the correct (reversed) positions, relative to each 10-bit groups of bits.

3. Together the multiply and the AND operations copy the bits from the original byte so they each appear in only one of the 10-bit sets. The reversed positions of the bits from the original byte coincide with their relative positions within any 10-bit set.

4. The last step (% 0x3ff), which involves modulus division by 2^10 - 1 has the effect of merging together each set of 10 bits (from positions 0-9, 10-19, 20-29, ...) in the 64-bit value. They do not overlap, so the addition steps underlying the modulus division behave like OR operations.

---

Divide and Conquer Solution

unsigned char reverse(unsigned char b) {
   b = (b & 0xF0) >> 4 | (b & 0x0F) << 4;
   b = (b & 0xCC) >> 2 | (b & 0x33) << 2;
   b = (b & 0xAA) >> 1 | (b & 0x55) << 1;
   return b;
}

This is the most upvoted answer and despite some explanations, I think that for most people it feels difficult to visualize whats 0xF0, 0xCC, 0xAA, 0x0F, 0x33 and 0x55 truly means.

It does not take advantage of '0b' which is a GCC extension and is included since the C++14 standard, release in December 2014, so a while after this answer dating from April 2010

Integer constants can be written as binary constants, consisting of a sequence of ‘0’ and ‘1’ digits, prefixed by ‘0b’ or ‘0B’. This is particularly useful in environments that operate a lot on the bit level (like microcontrollers).

Please check below code snippets to remember and understand even better this solution where we move half by half:

unsigned char reverse(unsigned char b) {
   b = (b & 0b11110000) >> 4 | (b & 0b00001111) << 4;
   b = (b & 0b11001100) >> 2 | (b & 0b00110011) << 2;
   b = (b & 0b10101010) >> 1 | (b & 0b01010101) << 1;
   return b;
}

NB: The >> 4 is because there are 8 bits in 1 byte, which is an unsigned char so we want to take the other half, and so on.

We could easily apply this solution to 4 bytes with only two additional lines and following the same logic. Since both mask complement each other we can even use ~ in order to switch bits and saving some ink:

uint32_t reverse_integer_bits(uint32_t b) {
   uint32_t mask = 0b11111111111111110000000000000000;
   b = (b & mask) >> 16 | (b & ~mask) << 16;
   mask = 0b11111111000000001111111100000000;
   b = (b & mask) >> 8 | (b & ~mask) << 8;
   mask = 0b11110000111100001111000011110000;
   b = (b & mask) >> 4 | (b & ~mask) << 4;
   mask = 0b11001100110011001100110011001100;
   b = (b & mask) >> 2 | (b & ~mask) << 2;
   mask = 0b10101010101010101010101010101010;
   b = (b & mask) >> 1 | (b & ~mask) << 1;
   return b;
}

---

[C++ Only] Reverse Any Unsigned (Template)

The above logic can be summarized with a loop that would work on any type of unsigned:

template <class T>
T reverse_bits(T n) {
    short bits = sizeof(n) * 8; 
    T mask = ~T(0); // equivalent to uint32_t mask = 0b11111111111111111111111111111111;
    
    while (bits >>= 1) {
        mask ^= mask << (bits); // will convert mask to 0b00000000000000001111111111111111;
        n = (n & ~mask) >> bits | (n & mask) << bits; // divide and conquer
    }

    return n;
}

---

C++ 17 only

You may use a table that store the reverse value of each byte with (i * 0x0202020202ULL & 0x010884422010ULL) % 0x3ff, initialized through a lambda (you will need to compile it with g++ -std=c++1z since it only works since C++17), and then return the value in the table will give you the accordingly reversed bit:

#include <cstdint>
#include <array>

uint8_t reverse_bits(uint8_t n) {
        static constexpr array<uint8_t, 256> table{[]() constexpr{
                constexpr size_t SIZE = 256;
                array<uint8_t, SIZE> result{};

                for (size_t i = 0; i < SIZE; ++i)
                    result[i] = (i * 0x0202020202ULL & 0x010884422010ULL) % 0x3ff;
                return result;
        }()};

    return table[n];
}

---

main.cpp

Try it yourself with inclusion of above function:

#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>

template <class T>
void print_binary(T n)
{   T mask = 1ULL << ((sizeof(n) * 8) - 1);  // will set the most significant bit
    for(; mask != 0; mask >>= 1) putchar('0' | !!(n & mask));
    putchar('\n');
}

int main() {
    uint32_t n = 12;
    print_binary(n);
    n = reverse_bits(n); 
    print_binary(n);
    unsigned char c = 'a';
    print_binary(c);
    c = reverse_bits(c);
    print_binary(c);
    uint16_t s = 12;
    print_binary(s);
    s = reverse_bits(s);
    print_binary(s);
    uint64_t l = 12;
    print_binary(l);
    l = reverse_bits(l);
    print_binary(l);
    return 0;
}

---

Reverse with asm volatile

Last but not least, if simplest means fewer lines, why not give a try to inline assembly?

You can test below code snippet by adding -masm=intel when compiling:

unsigned char reverse_bits(unsigned char c) {
    __asm__ __volatile__ (R"(
        mov cx, 8       
    daloop:                   
        ror di          
        adc ax, ax      
        dec cx          
        jnz short daloop  
    ;)");
}

Explanations line by line:

        mov cx, 8       ; we will reverse the 8 bits contained in one byte
    daloop:             ; while loop
        shr di          ; Shift Register `di` (containing value of the first argument of callee function) to the Right
        rcl ax          ; Rotate Carry Left: rotate ax left and add the carry from shr di, the carry is equal to 1 if one bit was "lost" from previous operation 
        dec cl          ; Decrement cx
        jnz short daloop; Jump if cx register is Not equal to Zero, else end loop and return value contained in ax register

Answer 8

Two lines:

for(i=0;i<8;i++)
     reversed |= ((original>>i) & 0b1)<<(7-i);

or in case you have issues with the "0b1" part:

for(i=0;i<8;i++)
     reversed |= ((original>>i) & 1)<<(7-i);

"original" is the byte you want to reverse. "reversed" is the result, initialized to 0.

Answer 9

Although probably not portable, I would use assembly language.
Many assembly languages have instructions to rotate a bit into the carry flag and to rotate the carry flag into the word (or byte).

The algorithm is:

for each bit in the data type:
  rotate bit into carry flag
  rotate carry flag into destination.
end-for

The high level language code for this is much more complicated, because C and C++ do not support rotating to carry and rotating from carry. The carry flag has to modeled.

Edit: Assembly language for example

;  Enter with value to reverse in R0.
;  Assume 8 bits per byte and byte is the native processor type.
   LODI, R2  8       ; Set up the bit counter
Loop:
   RRC, R0           ; Rotate R0 right into the carry bit.
   RLC, R1           ; Rotate R1 left, then append carry bit.
   DJNZ, R2  Loop    ; Decrement R2 and jump if non-zero to "loop"
   LODR, R0  R1      ; Move result into R0.

Answer 10

I find the following solution simpler than the other bit fiddling algorithms I've seen in here.

unsigned char reverse_byte(char a)
{

  return ((a & 0x1)  << 7) | ((a & 0x2)  << 5) |
         ((a & 0x4)  << 3) | ((a & 0x8)  << 1) |
         ((a & 0x10) >> 1) | ((a & 0x20) >> 3) |
         ((a & 0x40) >> 5) | ((a & 0x80) >> 7);
}

It gets every bit in the byte, and shifts it accordingly, starting from the first to the last.

Explanation:

   ((a & 0x1) << 7) //get first bit on the right and shift it into the first left position 
 | ((a & 0x2) << 5) //add it to the second bit and shift it into the second left position
  //and so on

Answer 11

The simplest way is probably to iterate over the bit positions in a loop:

unsigned char reverse(unsigned char c) {
   int shift;
   unsigned char result = 0;
   for (shift = 0; shift < CHAR_BIT; shift++) {
      if (c & (0x01 << shift))
         result |= (0x80 >> shift);
   }
   return result;
}

Answer 12

For the very limited case of constant, 8-bit input, this method costs no memory or CPU at run-time:

#define MSB2LSB(b) (((b)&1?128:0)|((b)&2?64:0)|((b)&4?32:0)|((b)&8?16:0)|((b)&16?8:0)|((b)&32?4:0)|((b)&64?2:0)|((b)&128?1:0))

I used this for ARINC-429 where the bit order (endianness) of the label is opposite the rest of the word. The label is often a constant, and conventionally in octal.

Here's how I used it to define a constant, because the spec defines this label as big-endian 205 octal.

#define LABEL_HF_COMM MSB2LSB(0205)

More examples:

assert(0b00000000 == MSB2LSB(0b00000000));
assert(0b10000000 == MSB2LSB(0b00000001));
assert(0b11000000 == MSB2LSB(0b00000011));
assert(0b11100000 == MSB2LSB(0b00000111));
assert(0b11110000 == MSB2LSB(0b00001111));
assert(0b11111000 == MSB2LSB(0b00011111));
assert(0b11111100 == MSB2LSB(0b00111111));
assert(0b11111110 == MSB2LSB(0b01111111));
assert(0b11111111 == MSB2LSB(0b11111111));
assert(0b10101010 == MSB2LSB(0b01010101));

Answer 13

You may be interested in std::vector<bool> (that is bit-packed) and std::bitset

It should be the simplest as requested.

#include <iostream>
#include <bitset>
using namespace std;
int main() {
  bitset<8> bs = 5;
  bitset<8> rev;
  for(int ii=0; ii!= bs.size(); ++ii)
    rev[bs.size()-ii-1] = bs[ii];
  cerr << bs << " " << rev << endl;
}

Other options may be faster.

EDIT: I owe you a solution using std::vector<bool>

#include <algorithm>
#include <iterator>
#include <iostream>
#include <vector>
using namespace std;
int main() {
  vector<bool> b{0,0,0,0,0,1,0,1};
  reverse(b.begin(), b.end());
  copy(b.begin(), b.end(), ostream_iterator<int>(cerr));
  cerr << endl;
}

The second example requires c++0x extension (to initialize the array with {...}). The advantage of using a bitset or a std::vector<bool> (or a boost::dynamic_bitset) is that you are not limited to bytes or words but can reverse an arbitrary number of bits.

HTH

Answer 14

Can this be fast solution?

int byte_to_be_reversed = 
    ((byte_to_be_reversed>>7)&0x01)|((byte_to_be_reversed>>5)&0x02)|      
    ((byte_to_be_reversed>>3)&0x04)|((byte_to_be_reversed>>1)&0x08)| 
    ((byte_to_be_reversed<<7)&0x80)|((byte_to_be_reversed<<5)&0x40)|
    ((byte_to_be_reversed<<3)&0x20)|((byte_to_be_reversed<<1)&0x10);

Gets rid of the hustle of using a for loop! but experts please tell me if this is efficient and faster?

Answer 15

Table lookup or

uint8_t rev_byte(uint8_t x) {
    uint8_t y;
    uint8_t m = 1;
    while (m) {
       y >>= 1;
       if (m&x) {
          y |= 0x80;
       }
       m <<=1;
    }
    return y;
}

edit

Look here for other solutions that might work better for you

Answer 16

a slower but simpler implementation:

static int swap_bit(unsigned char unit)
{
    /*
     * swap bit[7] and bit[0]
     */
    unit = (((((unit & 0x80) >> 7) ^ (unit & 0x01)) << 7) | (unit & 0x7f));
    unit = (((((unit & 0x80) >> 7) ^ (unit & 0x01))) | (unit & 0xfe));
    unit = (((((unit & 0x80) >> 7) ^ (unit & 0x01)) << 7) | (unit & 0x7f));

    /*
     * swap bit[6] and bit[1]
     */
    unit = (((((unit & 0x40) >> 5) ^ (unit & 0x02)) << 5) | (unit & 0xbf));
    unit = (((((unit & 0x40) >> 5) ^ (unit & 0x02))) | (unit & 0xfd));
    unit = (((((unit & 0x40) >> 5) ^ (unit & 0x02)) << 5) | (unit & 0xbf));

    /*
     * swap bit[5] and bit[2]
     */
    unit = (((((unit & 0x20) >> 3) ^ (unit & 0x04)) << 3) | (unit & 0xdf));
    unit = (((((unit & 0x20) >> 3) ^ (unit & 0x04))) | (unit & 0xfb));
    unit = (((((unit & 0x20) >> 3) ^ (unit & 0x04)) << 3) | (unit & 0xdf));

    /*
     * swap bit[4] and bit[3]
     */
    unit = (((((unit & 0x10) >> 1) ^ (unit & 0x08)) << 1) | (unit & 0xef));
    unit = (((((unit & 0x10) >> 1) ^ (unit & 0x08))) | (unit & 0xf7));
    unit = (((((unit & 0x10) >> 1) ^ (unit & 0x08)) << 1) | (unit & 0xef));

    return unit;
}

Answer 17

Before implementing any algorithmic solution, check the assembly language for whatever CPU architecture you are using. Your architecture may include instructions which handle bitwise manipulations like this (and what could be simpler than a single assembly instruction?).

If such an instruction is not available, then I would suggest going with the lookup table route. You can write a script/program to generate the table for you, and the lookup operations would be faster than any of the bit-reversing algorithms here (at the cost of having to store the lookup table somewhere).

Answer 18

This simple function uses a mask to test each bit in the input byte and transfer it into a shifting output:

char Reverse_Bits(char input)
{    
    char output = 0;

    for (unsigned char mask = 1; mask > 0; mask <<= 1)
    {
        output <<= 1;

        if (input & mask)
            output |= 1;
    }

    return output;
}

Answer 19

Assuming that your compiler allows unsigned long long:

unsigned char reverse(unsigned char b) {
  return (b * 0x0202020202ULL & 0x010884422010ULL) % 1023;
}

Discovered here

Answer 20

This one is based on the one BobStein-VisiBone provided

#define reverse_1byte(b)    ( ((uint8_t)b & 0b00000001) ? 0b10000000 : 0 ) | \
                            ( ((uint8_t)b & 0b00000010) ? 0b01000000 : 0 ) | \
                            ( ((uint8_t)b & 0b00000100) ? 0b00100000 : 0 ) | \
                            ( ((uint8_t)b & 0b00001000) ? 0b00010000 : 0 ) | \
                            ( ((uint8_t)b & 0b00010000) ? 0b00001000 : 0 ) | \
                            ( ((uint8_t)b & 0b00100000) ? 0b00000100 : 0 ) | \
                            ( ((uint8_t)b & 0b01000000) ? 0b00000010 : 0 ) | \
                            ( ((uint8_t)b & 0b10000000) ? 0b00000001 : 0 ) 

I really like this one a lot because the compiler automatically handle the work for you, thus require no further resources.

this can also be extended to 16-Bits...

#define reverse_2byte(b)    ( ((uint16_t)b & 0b0000000000000001) ? 0b1000000000000000 : 0 ) | \
                            ( ((uint16_t)b & 0b0000000000000010) ? 0b0100000000000000 : 0 ) | \
                            ( ((uint16_t)b & 0b0000000000000100) ? 0b0010000000000000 : 0 ) | \
                            ( ((uint16_t)b & 0b0000000000001000) ? 0b0001000000000000 : 0 ) | \
                            ( ((uint16_t)b & 0b0000000000010000) ? 0b0000100000000000 : 0 ) | \
                            ( ((uint16_t)b & 0b0000000000100000) ? 0b0000010000000000 : 0 ) | \
                            ( ((uint16_t)b & 0b0000000001000000) ? 0b0000001000000000 : 0 ) | \
                            ( ((uint16_t)b & 0b0000000010000000) ? 0b0000000100000000 : 0 ) | \
                            ( ((uint16_t)b & 0b0000000100000000) ? 0b0000000010000000 : 0 ) | \
                            ( ((uint16_t)b & 0b0000001000000000) ? 0b0000000001000000 : 0 ) | \
                            ( ((uint16_t)b & 0b0000010000000000) ? 0b0000000000100000 : 0 ) | \
                            ( ((uint16_t)b & 0b0000100000000000) ? 0b0000000000010000 : 0 ) | \
                            ( ((uint16_t)b & 0b0001000000000000) ? 0b0000000000001000 : 0 ) | \
                            ( ((uint16_t)b & 0b0010000000000000) ? 0b0000000000000100 : 0 ) | \
                            ( ((uint16_t)b & 0b0100000000000000) ? 0b0000000000000010 : 0 ) | \
                            ( ((uint16_t)b & 0b1000000000000000) ? 0b0000000000000001 : 0 ) 

Answer 21

Here is a simple and readable solution, portable to all conformant platforms, including those with sizeof(char) == sizeof(int):

#include <limits.h>

unsigned char reverse(unsigned char c) {
    int shift;
    unsigned char result = 0;

    for (shift = 0; shift < CHAR_BIT; shift++) {
        result <<= 1;
        result |= c & 1;
        c >>= 1;
    }
    return result;
}

Answer 22

If you using small microcontroller and need high speed solution with small footprint, this could be solutions. It is possible to use it for C project, but you need to add this file as assembler file *.asm, to your C project. Instructions: In C project add this declaration:

extern uint8_t byte_mirror(uint8_t);

Call this function from C

byteOutput= byte_mirror(byteInput);

This is the code, it is only suitable for 8051 core. In the CPU register r0 is data from byteInput. Code rotate right r0 cross carry and then rotate carry left to r1. Repeat this procedure 8 times, for every bit. Then the register r1 is returned to c function as byteOutput. In 8051 core is only posibble to rotate acumulator a.

NAME     BYTE_MIRROR
RSEG     RCODE
PUBLIC   byte_mirror              //8051 core        

byte_mirror
    mov r3,#8;
loop:   
    mov a,r0;
    rrc a;
    mov r0,a;    
    mov a,r1;
    rlc a;   
    mov r1,a;
    djnz r3,loop
    mov r0,a
    ret

PROS: It is small footprint, it is high speed CONS: It is not reusable code, it is only for 8051

011101101->carry

101101110<-carry

Answer 23

It is simple and fast:

unsigned char reverse(unsigned char rv)
{
unsigned char tmp=0;
if( rv&0x01 ) tmp = 0x80;
if( rv&0x02 ) tmp |= 0x40;
if( rv&0x04 ) tmp |= 0x20;
if( rv&0x08 ) tmp |= 0x10;
if( rv&0x10 ) tmp |= 0x08;
if( rv&0x20 ) tmp |= 0x04;
if( rv&0x40 ) tmp |= 0x02;
if( rv&0x80 ) tmp |= 0x01;
return tmp;
}

Answer 24

This is a similar method to sth's excellent answer, but with optimizations, support for up to 64-bit integers, and other small improvements.

I utilize a C++ template function reverse_bits() to let the compiler optimize for various word sizes of integers which might be passed to the function. The function should work correctly with any word size that is a multiple of 8 bits, up to a maximum of 64 bits. If your compiler supports words longer than 64 bits, the method is straightforward to extend.

This a complete, ready-to-compile example with the requisite headers. There is a convenient template function to_binary_str() for creating a std::string representation of binary numbers, along with a few calls with various word sizes to demonstrate everything.

If you remove the comments and blank lines, the function is quite compact and visually pleasing.

You can try out it on labstack here.

// this is the only header used by the reverse_bits() function
#include <type_traits>

// these headers are only used by demonstration code
#include <string>
#include <iostream>
#include <cstdint>


template<typename T>
T reverse_bits( T n ) {
    // we force the passed-in type to its unsigned equivalent, because C++ may
    // perform arithmetic right shift instead of logical right shift, depending
    // on the compiler implementation.
    typedef typename std::make_unsigned<T>::type unsigned_T;
    unsigned_T v = (unsigned_T)n;

    // swap every bit with its neighbor
    v = ((v & 0xAAAAAAAAAAAAAAAA) >> 1)  | ((v & 0x5555555555555555) << 1);

    // swap every pair of bits
    v = ((v & 0xCCCCCCCCCCCCCCCC) >> 2)  | ((v & 0x3333333333333333) << 2);

    // swap every nybble
    v = ((v & 0xF0F0F0F0F0F0F0F0) >> 4)  | ((v & 0x0F0F0F0F0F0F0F0F) << 4);
    // bail out if we've covered the word size already
    if( sizeof(T) == 1 ) return v;

    // swap every byte
    v = ((v & 0xFF00FF00FF00FF00) >> 8)  | ((v & 0x00FF00FF00FF00FF) << 8);
    if( sizeof(T) == 2 ) return v;

    // etc...
    v = ((v & 0xFFFF0000FFFF0000) >> 16) | ((v & 0x0000FFFF0000FFFF) << 16);
    if( sizeof(T) <= 4 ) return v;

    v = ((v & 0xFFFFFFFF00000000) >> 32) | ((v & 0x00000000FFFFFFFF) << 32);

    // explictly cast back to the original type just to be pedantic
    return (T)v;
}


template<typename T>
std::string to_binary_str( T n ) {
    const unsigned int bit_count = sizeof(T)*8;
    char s[bit_count+1];
    typedef typename std::make_unsigned<T>::type unsigned_T;
    unsigned_T v = (unsigned_T)n;
    for( int i = bit_count - 1; i >= 0; --i ) {
        if( v & 1 )
            s[i] = '1';
        else
            s[i] = '0';

        v >>= 1;
    }
    s[bit_count] = 0;  // string null terminator
    return s;
}


int main() {
    {
        char x = 0xBA;
        std::cout << to_binary_str( x ) << std::endl;

        char y = reverse_bits( x );
        std::cout << to_binary_str( y ) << std::endl;
    }
    {
        short x = 0xAB94;
        std::cout << to_binary_str( x ) << std::endl;

        short y = reverse_bits( x );
        std::cout << to_binary_str( y ) << std::endl;
    }
    {
        uint64_t x = 0xFEDCBA9876543210;
        std::cout << to_binary_str( x ) << std::endl;

        uint64_t y = reverse_bits( x );
        std::cout << to_binary_str( y ) << std::endl;
    }
    return 0;
}

Answer 25

With the help of various online resources, i jotted these for myself (not sure if they're 100% accurate) :

#                 octal       hex

# bit-orig    : 01234567    01234567:89ABCDEF
# bit-invert  : 76543210    FEDCBA98:76543210
#
# clz         : 32110000    43221111:00000000
# clo/ffs     : 00001123    00000000:11112234

bit-reverse : [ 0 4 2 6 1 5 3 7 ] [ 0 8 4 C 2 A 6 E 1 9 5 D 3 B 7 F ]

# cto         : 01020103    01020103:01020104
# ctz         : 30102010    40102010:30102010

but this is mostly only convenient if your input is already either hex or octal.

In both formats (8 or 16), you'll notice that after the bit-reflections, all the even number indices are all on the first half. I've also highlighted the same 0-7 on the hex side to help with the visualization of it.

in fact, one doesn't even have to do a double substring. The lookup string can be either used as seeking the letter needed, or simply use it as an index lookup. this is how i reflect the CRC32 polynomial myself :

(z is the input polynomial (or just any hex string)

xn = 0 ^ (x = length(z));          # initialize to numeric 0,
                                   # foo^bar in awk means 
                                   # foo-to-bar-th-power. 
                                   # same as foo**bar in other langs

 y = substr(_REF_bitREV_hex, 2);   # by pre-trimming the lookup str,
                                   # it allows skipping the + 1 at            
                                   # every cycle of the loop
 do { 
     xn *= 16
     xn += index(y, substr(z,x,1)) # keep in mind that this is awk syntax, 
                                   # where strings start at index-1, not zero.
 } while ( 1 < x—- );

One advantage of using a hex- or octal- based approach is that it allows for inputs of any length, enabling arbitrary precision operation without having to use a proper BigInteger or BigFloat library. For that, you'll have to substring out the new digit/letter and do string concats instead of simply adding each time.

Answer 26

If there is one wondering how to get uint16_t or uint32_t bit reversed by using the solution from Rich Schroeppel in the Programming Hacks section

unsigned char reverse_bits3(unsigned char b)
{
    return (b * 0x0202020202ULL & 0x010884422010ULL) % 0x3ff;
}

It can be done by following divide-and-conquer code on X86/X64 platform (little-endian):

uint16_t reverse_bits3(uint16_t s)
{
    uint8_t &b0 = ((uint8_t*)&s)[0];
    uint8_t &b1 = ((uint8_t*)&s)[1];
    return (((uint16_t)reverse_bits3(b0))<<8) + reverse_bits3(b1);
}

uint32_t reverse_bits3(uint32_t u)
{
    uint16_t &s0 = ((uint16_t*)&u)[0];
    uint16_t &s1 = ((uint16_t*)&u)[1];
    return (((uint16_t)reverse_bits3(s0))<<16) + reverse_bits3(s1);
}

Answer 27

I'll chip in my solution, since i can't find anything like this in the answers so far. It is a bit overengineered maybe, but it generates the lookup table using C++14 std::index_sequence in compile time.

#include <array>
#include <utility>

constexpr unsigned long reverse(uint8_t value) {
    uint8_t result = 0;
    for (std::size_t i = 0, j = 7; i < 8; ++i, --j) {
        result |= ((value & (1 << j)) >> j) << i;
    }
    return result;
}

template<size_t... I>
constexpr auto make_lookup_table(std::index_sequence<I...>)
{
    return std::array<uint8_t, sizeof...(I)>{reverse(I)...};   
}

template<typename Indices = std::make_index_sequence<256>>
constexpr auto bit_reverse_lookup_table()
{
    return make_lookup_table(Indices{});
}

constexpr auto lookup = bit_reverse_lookup_table();

int main(int argc)
{
    return lookup[argc];
}

https://godbolt.org/z/cSuWhF

Answer 28

I know that this question is dated but I still think that the topic is relevant for some purposes, and here is a version that works very well and is readable. I can not say that it is the fastest or the most efficient, but it ought to be one of the cleanest. I have also included a helper function for easily displaying the bit patterns. This function uses some of the standard library functions instead of writing your own bit manipulator.

#include <algorithm>
#include <bitset>
#include <exception>
#include <iostream>
#include <limits>
#include <string>

// helper lambda function template
template<typename T>
auto getBits = [](T value) {
    return std::bitset<sizeof(T) * CHAR_BIT>{value};
};

// Function template to flip the bits
// This will work on integral types such as int, unsigned int,
// std::uint8_t, 16_t etc. I did not test this with floating
// point types. I chose to use the `bitset` here to convert
// from T to string as I find it easier to use than some of the
// string to type or type to string conversion functions,
// especially when the bitset has a function to return a string. 
template<typename T>
T reverseBits(T& value) {
    static constexpr std::uint16_t bit_count = sizeof(T) * CHAR_BIT;

    // Do not use the helper function in this function!
    auto bits = std::bitset<bit_count>{value};
    auto str = bits.to_string();
    std::reverse(str.begin(), str.end());
    bits = std::bitset<bit_count>(str);
    return static_cast<T>( bits.to_ullong() );
}

// main program
int main() {
    try {
        std::uint8_t value = 0xE0; // 1110 0000;
        std::cout << +value << '\n'; // don't forget to promote unsigned char
        // Here is where I use the helper function to display the bit pattern
        auto bits = getBits<std::uint8_t>(value);
        std::cout << bits.to_string() << '\n';

        value = reverseBits(value);
        std::cout << +value << '\n'; // + for integer promotion

        // using helper function again...
        bits = getBits<std::uint8_t>(value);
        std::cout << bits.to_string() << '\n';

    } catch(const std::exception& e) {  
        std::cerr << e.what();
        return EXIT_FAILURE;
    }
    return EXIT_SUCCESS;
}

And it gives the following output.

224
11100000
7
00000111

Answer 29

This one helped me with 8x8 dot matrix set of arrays.

uint8_t mirror_bits(uint8_t var)
{
    uint8_t temp = 0;
    if ((var & 0x01))temp |= 0x80;
    if ((var & 0x02))temp |= 0x40;
    if ((var & 0x04))temp |= 0x20;
    if ((var & 0x08))temp |= 0x10;

    if ((var & 0x10))temp |= 0x08;
    if ((var & 0x20))temp |= 0x04;
    if ((var & 0x40))temp |= 0x02;
    if ((var & 0x80))temp |= 0x01;

    return temp;
}

Answer 30

regarding the bit-reflected lookup table for all 256 bytes, with just a few loops, you can generate it from scratch on the fly very quickly (the mapping from hex to bytes should be trivial) :

 #  gawk profile,created Tue Jul 26 22:22:18 2022

 #  BEGIN rule(s)
    BEGIN {
 1      print initREF()
    }
 # Functions,listed alphabetically
 1  function initREF(_,__,___,____,_____,______,_______)
    {
 1     ______=(_+=_^=_<_)^++_-(_=\
           __=(+(___=____="."))(_~_))

 1     gsub(___,"&\\&",_)
 1     _____[_<_]
       _____[ +_]

 7     do {
 7         gsub(___,_,__)
 7         ___=___""____
       } while (—______)

 1     gsub("....","=&", __)
 1     _+=_^=_<_;_______=__;

 2     for(______ in _____) { ______*=_*_*_
 4        for(____ in _____) {  ____*=_+_
 8           for(___ in _____) { ___*= +_
16              for(__ in _____) {

16                    gsub("=" (_<______)(_<____) (_~___)__,
                   sprintf("%X", __+___+____+______),_______)
        } } } }

 1      __=_______
 1       _="[^ ]+[ ]"
 1      gsub(".",_,_)

 1      gsub("..","0x&, ",__)
 1      gsub((_)_,  "&\n",__)
 1      sub("[\1-@]+$","",__)
 1            gsub(" ","",__)

 1      return __
    }

|

0x00,0x80,0x40,0xC0,0x20,0xA0,0x60,0xE0,0x10,0x90,0x50,0xD0,0x30,0xB0,0x70,0xF0,
0x08,0x88,0x48,0xC8,0x28,0xA8,0x68,0xE8,0x18,0x98,0x58,0xD8,0x38,0xB8,0x78,0xF8,
0x04,0x84,0x44,0xC4,0x24,0xA4,0x64,0xE4,0x14,0x94,0x54,0xD4,0x34,0xB4,0x74,0xF4,
0x0C,0x8C,0x4C,0xCC,0x2C,0xAC,0x6C,0xEC,0x1C,0x9C,0x5C,0xDC,0x3C,0xBC,0x7C,0xFC,
0x02,0x82,0x42,0xC2,0x22,0xA2,0x62,0xE2,0x12,0x92,0x52,0xD2,0x32,0xB2,0x72,0xF2,
0x0A,0x8A,0x4A,0xCA,0x2A,0xAA,0x6A,0xEA,0x1A,0x9A,0x5A,0xDA,0x3A,0xBA,0x7A,0xFA,
0x06,0x86,0x46,0xC6,0x26,0xA6,0x66,0xE6,0x16,0x96,0x56,0xD6,0x36,0xB6,0x76,0xF6,
0x0E,0x8E,0x4E,0xCE,0x2E,0xAE,0x6E,0xEE,0x1E,0x9E,0x5E,0xDE,0x3E,0xBE,0x7E,0xFE,
0x01,0x81,0x41,0xC1,0x21,0xA1,0x61,0xE1,0x11,0x91,0x51,0xD1,0x31,0xB1,0x71,0xF1,
0x09,0x89,0x49,0xC9,0x29,0xA9,0x69,0xE9,0x19,0x99,0x59,0xD9,0x39,0xB9,0x79,0xF9,
0x05,0x85,0x45,0xC5,0x25,0xA5,0x65,0xE5,0x15,0x95,0x55,0xD5,0x35,0xB5,0x75,0xF5,
0x0D,0x8D,0x4D,0xCD,0x2D,0xAD,0x6D,0xED,0x1D,0x9D,0x5D,0xDD,0x3D,0xBD,0x7D,0xFD,
0x03,0x83,0x43,0xC3,0x23,0xA3,0x63,0xE3,0x13,0x93,0x53,0xD3,0x33,0xB3,0x73,0xF3,
0x0B,0x8B,0x4B,0xCB,0x2B,0xAB,0x6B,0xEB,0x1B,0x9B,0x5B,0xDB,0x3B,0xBB,0x7B,0xFB,
0x07,0x87,0x47,0xC7,0x27,0xA7,0x67,0xE7,0x17,0x97,0x57,0xD7,0x37,0xB7,0x77,0xF7,
0x0F,0x8F,0x4F,0xCF,0x2F,0xAF,0x6F,0xEF,0x1F,0x9F,0x5F,0xDF,0x3F,0xBF,0x7F,0xFF

Answer 31

This is the easiest approach to remember to me as a developer:

unsigned char   reverse_bits(unsigned char octet)
    {
        return  (((octet >> 0) & 1) << 7) | \
                (((octet >> 1) & 1) << 6) | \
                (((octet >> 2) & 1) << 5) | \
                (((octet >> 3) & 1) << 4) | \
                (((octet >> 4) & 1) << 3) | \
                (((octet >> 5) & 1) << 2) | \
                (((octet >> 6) & 1) << 1) | \
                (((octet >> 7) & 1) << 0);
    }
 

Answer 32

The easiest and fast way is with while

#define REVERSE_NUMBER(n, res) while (n) \
    { res = (res << 1) + (n % 2); n >>= 1; }

unsigned int res; //res is result
unsigned int n = 0x135F; // n = 1001101011111

REVERSE_NUMBER(n, res);  // res = 1111101011001 (1F59)

or with function

unsigned int reverse_number(unsigned int n) {
    unsigned int res;
    while (n) {
        res = (res << 1) + (n % 2);
        n >>= 1;
    }
    return res;
}

even easier way and effective

// shift << and >> equivalent to multiplication and division by 2
// and bitwise & 1 equivalent mod by 2
unsigned int reverse_number(unsigned int n) {
    unsigned int res = 0;
    size_t i = sizeof(unsigned int) * 8; // 32 bit value
    while (i--) {
        res = (res << 1) + (n & 1); n >>= 1;
    }
    return res;
}

Answer 33

#include <stdio.h>
#include <stdlib.h>

int main()
{
    int i;
    unsigned char rev = 0x70 ; // 0b01110000
    unsigned char tmp = 0;

    for(i=0;i<8;i++)
    {
    tmp |= ( ((rev & (1<<i))?1:0) << (7-i));
    }
    rev = tmp;

    printf("%x", rev);       //0b00001110 binary value of given number
    return 0;
}

Answer 34

#define BITS_SIZE 8

int
reverseBits ( int a )
{
  int rev = 0;
  int i;

  /* scans each bit of the input number*/
  for ( i = 0; i < BITS_SIZE - 1; i++ )
  {
    /* checks if the bit is 1 */
    if ( a & ( 1 << i ) )
    {
      /* shifts the bit 1, starting from the MSB to LSB
       * to build the reverse number 
      */
      rev |= 1 << ( BITS_SIZE - 1 ) - i;
    }
  }

  return rev;
}

Answer 35

  xor ax,ax
  xor bx,bx
  mov cx,8
  mov al,original_byte!
cycle:   shr al,1
  jnc not_inc
  inc bl
not_inc: test cx,cx
  jz,end_cycle
  shl bl,1
  loop cycle
end_cycle:

reversed byte will be at bl register

Answer 36

typedef struct
{
    uint8_t b0:1;
    uint8_t b1:1;
    uint8_t b2:1;
    uint8_t b3:1;
    uint8_t b4:1;
    uint8_t b5:1;
    uint8_t b6:1;
    uint8_t b7:1;
} bits_t;

uint8_t reverse_bits(uint8_t src)
{
    uint8_t dst = 0x0;
    bits_t *src_bits = (bits_t *)&src;
    bits_t *dst_bits = (bits_t *)&dst;

    dst_bits->b0 = src_bits->b7;
    dst_bits->b1 = src_bits->b6;
    dst_bits->b2 = src_bits->b5;
    dst_bits->b3 = src_bits->b4;
    dst_bits->b4 = src_bits->b3;
    dst_bits->b5 = src_bits->b2;
    dst_bits->b6 = src_bits->b1;
    dst_bits->b7 = src_bits->b0;

    return dst;
}

Answer 37

I think this is simple enough

uint8_t reverse(uint8_t a)
{
  unsigned w = ((a << 7) & 0x0880) | ((a << 5) & 0x0440) | ((a << 3) & 0x0220) | ((a << 1) & 0x0110);
  return static_cast<uint8_t>(w | (w>>8));
}

or

uint8_t reverse(uint8_t a)
{
  unsigned w = ((a & 0x11) << 7) | ((a & 0x22) << 5) | ((a & 0x44) << 3) | ((a & 0x88) << 1);
  return static_cast<uint8_t>(w | (w>>8));
}

Answer 38

unsigned char c ; // the original
unsigned char u = // the reversed
c>>7&0b00000001 |
c<<7&0b10000000 |
c>>5&0b00000010 |
c<<5&0b01000000 |
c>>3&0b00000100 |
c<<3&0b00100000 |
c>>1&0b00001000 |
c<<1&0b00010000 ;

Explanation: exchanged bits as per the arrows below.
01234567
<------>
#<---->#
##<-->##
###<>###

Answer 39

#include <stdio.h>
#include <stdlib.h>

#define BIT0 (0x01)
#define BIT1 (0x02)
#define BIT2 (0x04)
#define BIT3 (0x08)
#define BIT4 (0x10)
#define BIT5 (0x20)
#define BIT6 (0x40)
#define BIT7 (0x80)

#define BYTE_TO_BINARY_PATTERN "%c%c%c%c%c%c%c%c\n"

#define BITETOBINARY(byte) \
(byte & BIT7 ? '1' : '0'), \
(byte & BIT6 ? '1' : '0'), \
(byte & BIT5 ? '1' : '0'), \
(byte & BIT4 ? '1' : '0'), \
(byte & BIT3 ? '1' : '0'), \
(byte & BIT2 ? '1' : '0'), \
(byte & BIT1 ? '1' : '0'), \
(byte & BIT0 ? '1' : '0') \

#define BITETOBINARYREVERSE(byte) \
(byte & BIT0 ? '1' : '0'), \
(byte & BIT1 ? '1' : '0'), \
(byte & BIT2 ? '1' : '0'), \
(byte & BIT3 ? '1' : '0'), \
(byte & BIT4 ? '1' : '0'), \
(byte & BIT5 ? '1' : '0'), \
(byte & BIT6 ? '1' : '0'), \
(byte & BIT7 ? '1' : '0') \



int main()
{

    int i,j,c;

    i |= BIT2|BIT7;

    printf("0x%02X\n",i);    

    printf(BYTE_TO_BINARY_PATTERN,BITETOBINARY(i));

    printf("Reverse");

    printf(BYTE_TO_BINARY_PATTERN,BITETOBINARYREVERSE(i));

   return 0;
}

Answer 40

This is an old question, but nobody seems to have shown the clear easy way (the closest was edW). I used C# to test this, but there's nothing in this example that couldn't be done easily in C.

void PrintBinary(string prompt, int num, int pad = 8)
{
    Debug.WriteLine($"{prompt}: {Convert.ToString(num, 2).PadLeft(pad, '0')}");
}

int ReverseBits(int num)
{
    int result = 0;
    int saveBits = num;
    for (int i = 1; i <= 8; i++)
    {
        // Move the result one bit to the left
        result = result << 1;

        //PrintBinary("saveBits", saveBits);

        // Extract the right-most bit
        var nextBit = saveBits & 1;

        //PrintBinary("nextBit", nextBit, 1);

        // Add our extracted bit to the result
        result = result | nextBit;

        //PrintBinary("result", result);

        // We're done with that bit, rotate it off the right
        saveBits = saveBits >> 1;

        //Debug.WriteLine("");
    }

    return result;
}

void PrintTest(int nextNumber)
{
    var result = ReverseBits(nextNumber);

    Debug.WriteLine("---------------------------------------");
    PrintBinary("Original", nextNumber);
    PrintBinary("Reverse", result);
}

void Main()
{
    // Calculate the reverse for each number between 1 and 255
    for (int x = 250; x < 256; x++)
        PrintTest(x);
}

Answer 41

How about this one...

int value = 0xFACE;

value = ((0xFF & value << 8) | (val >> 8);

Answer 42

How about just XOR the byte with 0xFF.

unsigned char reverse(unsigned char b) { b ^= 0xFF; return b; }