MATLAB: Binary addition in MATLAB

Question

Is it possible to do binary addition in MATLAB? I tried using the usual add function but it didnt work. I defined 2 numbers as binary digits, say 1010 and 1100. The output came out as 2100. It's a direct addition of 2 numbers.

Answer 1

You need to see the Fixed Point Toolbox.

You need to see it because it requires you to make explicit numerous assumptions about your arithmetic.

For example, since you used 1010 and 1100 and not (say) 00001010 and 00001100, then we don't know whether you simply used "leading 0 suppression" or if you mean to restrict your arithmetic to 4 digits. If you mean to restrict your arithmetic to 4 digits, then you need to define whether upon overflow (such as you get here) you want the overflowing bits to be discarded or you want to "saturate" to the highest possible representable value 1111 . Your addition is thus answerable by a minimum of 3 different values: 10110, 0110, and 1111.

But then there is the difficulty that when you use binary, the '+' operator often means "or", which would give you the additional possible answer 1110.

More generally, are the values to be added 52 bits long or less? If so then their sum is exactly representable in a double precision number for fast calculations. But as soon as you go to 53 bits, the sum might need 54 bits: sums that occupy 54 through 64 bits can only be done directly in R2010b or later, unless through the Fixed Point Toolbox.