Page 95 - Bebop to The Boolean Boogie An Unconventional Guide to Electronics Fundamentals, Components, and Processes

76 w Chapter Eight

closer investigation reveals that each bit pattern is in fact the twos complement
of the other! To put this another way, taking the twos complement of a positive
signed binary value returns its negative equivalent and vice versa.
The end result is that using signed binary numbers greatly reduces the
complexity of operations within a computer. To illustrate why this is so, first
consider one of the simplest operations, that of addition. Compare the additions
of positive and negative decimal values in sign-magnitude form with their
signed binary counterparts (Figure 8-10).
Examine the standard decimal calculations on the left. The one at the top
is easy to understand because it’s a straightforward addition of two positive
values. However, even though you are familiar with decimal addition, you
probably found the other three a little harder because you had to decide
exactly what to do with the negative values. By comparison, the signed binary

Decimal sign- Signed binary
magnitude
57 00111001
+ 30 ‘+00011110
= 07 01010111

57 00111001
+ -3 0 +11100010
= 27 00011011

-5 7 11000111
+ 30 +00011110

= -2 7 11100101

-5 7 11000111
+ -3 0 +11100010
= -0 7 10101001

Figure 8-1 0. Comparison of sign-magnitude
versus signed binary additions