How to subtract in binary
Remember how subtraction works. We work from the least-significant bits to the most-significant, and pairwise subtract them. 1-1=0, 1-0=1, 0-0=0.
But 0-1 presents a problem: it’s negative 1. We represent this by outputting 1 and carrying a 1 to be subtracted from the next bits. We end up with the following logic table. It shows inputs CI (carry in), A (the bit being subtracted from), and B (the bit to subtract). These are mapped to outputs CO (carry out) and O (output).
(Inputs) | (Outputs)
CI A B | CO O
== == == | == ==
0 0 0 | 0 0
0 0 1 | 1 1
0 1 0 | 0 1
0 1 1 | 0 0
1 0 0 | 1 1
1 0 1 | 1 0
1 1 0 | 0 0
1 1 1 | 1 1
The meaning here is that CO and O together represent the result of A - (B+CI). This is a number between -2 and 1. Here’s the meaning:
CO O | Meaning
== == | =======
0 0 | 0
0 1 | 1
1 0 | -2
1 1 | -1
This is not arbitrary. The relation is that Meaning = ( CO * -2) + O. This is precisely “two’s complement representation”: CO and O placed side-by-side are the two’s complement representation of the number.
Tagged . All content copyright James Fisher 2017. This post is not associated with my employer.
TigYog