Convert signed two's complement binary to decimal

Question

So i have to convert two's complement binary to decimal in C++ by first inserting the number of bits user wants to use 1 by one for example: Bits: 4

Insert the bit in position 3: 1

Insert the bit in position 2: 0

Insert the bit in position 1: 0

Insert the bit in position 0: 0

I have done the code for this using an array and then using for to store a[i]. I'm stuck and i dont know what to do to convert it to decimal. I would appreciate any help thanks.

int main() {
int n;
cout << "Bits: " << endl;
cin >> n;

while (n < 2) {
    cout << "Error! " << endl;
    cout << "Bits: " << endl;
    cin >> n;
}
int a[10000];

for (int i = n; i > 0; i--) {
    cout << "Insert the bit in position " << i - 1 << ": " << endl;
    cin >> a[i];
    while (a[i] != 0 && a[i] != 1) {
        cout << "Error! " << endl;
        cout << "Insert the bit in position " << i - 1 << ": " << endl;
        cin >> a[i];
    }
}

int choice;

cout << "Operation: " << endl;
cout << "      0 - Print binary: " << endl;
cout << "      1 - Convert in decimal: " << endl;


cout << "Choice: ";
cin >> choice;
cout << endl;

switch (choice) {
    case 0:
        cout << "Binary number: ";
        for (int i = n; i > 0; i--)
            cout << a[i];
        cout << endl;
        break;

Hint: A binary number is `bn*2^n + bn-1*2^n-1 + ... + b0*2^0` — NathanOliver, Nov 02 '22 at 15:38
[What is a debugger and how can it help me diagnose problems?](https://stackoverflow.com/questions/25385173/what-is-a-debugger-and-how-can-it-help-me-diagnose-problems) — Jason, Nov 02 '22 at 15:48
Please scale down your code to produce a [example] with a binary array and attempt to convert it to decimal. — CausingUnderflowsEverywhere, Nov 04 '22 at 01:51

selbie · Answer 1 · 2022-11-02T22:17:43.773

To convert your a array from a list of 0 and 1 integers to unsigned decimal:

unsigned long sum = 0;
for (int i = 0; i < n; i++)
{
    sum = sum*2 + a[i];
}

If you are expected to interpret these bits as signed values such that 11001100 would be interpreted as -52 instead of 204. You will need to do the following:

First check if a[0] == 0. If it is, then all you need to do is the summation loop above and you are done. You can print sum as is.
Otherwise, if a[1] == 1, then that implies this is a negative number and we need to do 2's complement to interpret it. Continue with the following:
Flip all the values in a (0's become 1s and 1s become 0's) from index 0 through n-1.
Arithmetically "add 1". You just need to reflip the bits in a starting at a[n-1] and work your way from right to left. Stop after flipping a 0 to 1.
Then apply the summation loop above to get the absolute value of the number. Then print a negative sign followed by the postive value computed for sum. You might be tempted to say, long negativeSum = -sum and just print that. And that will work most of the time, except there's an edge case.

I'll leave the actual coding as an exercise for you.

Convert signed two's complement binary to decimal

1 Answers1