LC-3 How to store a number large than 16-bit and print it out to console?

Question

I'm having difficulty storing and displaying numbers greater than 32767 in LC-3 since a register can only hold values from -32768 to 32767. My apology for not being able to come up with any idea for the algorithm. Please give me some suggestion. Thanks!

Answer 1

You'll need a representation to store the larger number in a pair or more of words.

There are several approaches to how big integers are stored: in a fixed number of words, and in a variable number of words or bytes.  The critical part is being able to detect the presence and amount of overflow/carry on mathematical operations like *10.

For that reason, one simple approach is to use a variable number of words/bytes (for a single number), and store only one decimal digit in each of the words/bytes.  That way multiplication by 10, means simply adding a digit on the end (which has the effect of moving each existing digit to the next higher power of ten position).  Adding numbers of this form numbers is fairly easy as well, we need to line up the digits and then, we add them up and detect when the sum is >= 10, then there is a carry (of 1) to be added to the next higher order digit of the sum.  (If adding two such (variable length) numbers is desired, I would store the decimal digits in reverse order, because then the low order numbers are already lined up for addition.)  See also https://en.wikipedia.org/wiki/Binary-coded_decimal .  (In some sense, this is like storing numbers in a form like string, but using binary values instead of ascii characters.)

To simplify this approach for your needs, you can fix the number of words to use, e.g. at 7, for 7 digits.

A variation on (unpacked) Binary-coded Decimal to pack them two decimal digits per byte.  Its a bit more complicated but saves some storage.

Another approach is to store as many decimal digits as will fit full in a word, minus 1.  Which is to say if we can store 65536 in 16-bits that's only 4 full decimal digits, which means putting 3 digits at a time into a word.  You'd need 3 words for 9 digits.  Multiplication by 10 means multiplying each word by 10 numerically, and then checking for larger than 999, and if larger, then carry the 1 to the next higher order word while also subtracting 10,000 from the overflowing word.

This approach will require actual multiplication and division by 10 on each of the individual words.

There are other approaches, such as using all 16-bits in a word as magnitude, but the difficulty there is determining the amount of overflow/carry on *10 operations.  It is not a monumental task but will require work.  See https://stackoverflow.com/a/1815371/471129, for example.

(If you also want to store negative numbers, that is also an issue for representation.  We can either store the sign as separately known as sign-magnitude form (as in stored its own word/byte or packed into the highest byte) or store the number in a compliment form.  The former is better for variable length implementations and the latter can be made to work for fixed length implementations.)