Page 88 - Bebop to The Boolean Boogie An Unconventional Guide to Electronics Fundamentals, Components, and Processes

Binary Arithmetic w 69
1
00 1 1 100 1 +ooo 110 1
1
00 1
100 1
+ooo 110 10 10
-
- 1 - 1 1
-
(a) Bit0, 1 + 0 = 1, (b) Bit 1, 0 +I =I,

+ooo 110 0 +000,110 1 10
00 1
100 1
1
100 1
00 1
1
10
- 011 - 00 1 1
-
-
(c) Bit 2, 0 + 0 = 0, (d) Bit 3, 1 + 1 =IO,

100 1
10 10
- - 1001 1 - - 0 100 1 1

(e) Bit 4,l + 1 + carry-in = 11, (f) Bit 5,l + 0 + carry-in = 10,

w

00 1 1 100 1 100 1 57,,

+o,o,o ,I 10 10 ,I 10 10 +26,,
- - 10 100 1 1 =o 10 100 1 1 = 03,,

(4) Bit 6,O + 0 + carry-in = 1, (h) Bit7, 0 + 0= 0,

Figure 8-2. Binary addition

carry-out occurs in step (e), where the carry-in from the previous stage results
in 1 + 1 + 1 = 3 or, in binary, 1, + 1, + 1, = 11,; thus, in this instance, the sum
is 1 and there is a carry-out of 1 to the next stage. The third and final carry-out
occurs in step (f), and it’s plain sailing from there on in.