Page 87 - Bebop to The Boolean Boogie An Unconventional Guide to Electronics Fundamentals, Components, and Processes

68 ChaptevEight

Z7 = 128’5 column = bit 7
26 = 64‘scolumn = bit6
Z5 = 32’5column = bit5
Z4 = 16‘scolumn = bit4
Z3 = 8’5 column = bit 3
Z2 = 4‘s column = bit 2
2’ = 2’5 column = bit 1
Z0 = 1’s column = bit 0

M56-x x x x x x x x bL56

00000000 = o,,
00000001 = I,,
00000010 = 2,,
0000001 1 = 3,,
00000100 = 4,,

1 1 1 1 1 1 0 1 =253,,
1 1 1 1 1 1 1 0 =254,,
1 1 1 1 1 1 1 1 =255,,

Figure 8-1. Unsigned binary numbers

Binary Addition
Two binary numbers may be added together using an identical process to
that used for decimal addition. First, the two least significant bits are added
together to give a sum and, possibly, a carry-out to the next stage. This process
is repeated for the remaining bits progressing towards the most significant. For
each of the remaining bits, there may be a carry-in from the previous stage and
a carry-out to the next stage. To fully illustrate this process, consider the step-
by-step addition of two 8-bit binary numbers (Figure 8-2).
We commence with the least significant bits in step (a), 1 + 0 = 1. In
step (b) we see 0 + 1 = 1, followed by 0 + 0 = 0 in step (c). The first carry-out
occurs in step (d), where 1 + 1 = 2 or, in binary, 1, + 1, = 10,; thus, in this
instance, the sum is 0 and there is a carry-out of 1 to the next stage. The second