Page 92 - Bebop to The Boolean Boogie An Unconventional Guide to Electronics Fundamentals, Components, and Processes

Binary Arithmetic 73

Standard subtraction
00 11 1001
-0001 11 10

=00011011

l100000000 001 11001 I
I-00011110 +111000101
I 11100010 10001 101 1
I=
I- 0001 101 1
I Take twos complement - 1
Add twos complement I
to minuend I
L--------------------~

Figure 8-6. Twos complement binary subtraction

As fate would have it, there is a short-cut approach available to generate
the twos complement of a binary number. Commencing with the least signifi-
cant bit of the value to be complemented, each bit up to and including the first
* *
1 is copied directly, and the remaining bits are inverted (Figure 8-7).
MSB L56

- _ _ - _ _ 1 0 I Copyfrom the L56 upto,
and including, the first 1

1 1 1 0 0 0 1 0 I lnvertthe remaining bits

Figure 8-7. Shortcut for generating a twos complement