Page 291 - Engineering Digital Design

262 CHAPTER 6 / NONARITHMETIC COMBINATIONAL LOGIC DEVICES

BCD Binary
—\
[) D D B B B B B Dec.
D 3 3 D 2 2 ' o u ».| B O Dec. \D 2D 1 \D 2D
4 » 2 1 1 "
P4D\ 00 01 11 10 D 4 D\ 00 01 11 10
0 0 0 0 0 0 0 0 0 0 0 00 0 00
0 0 0 0 1 0 0 0 0 1 1
0 0 0 1 0 0 0 0 1 0 2 01 0 01 d
0 0 0 1 1 0 0 0 1 1 3
0 0 1 0 0 0 0 1 0 0 4 11 11
0 0 1 0 1 0 0 1 0 1 5
10 10
0 0 1 1 0 0 0 1 1 0 6
0 0 1 1 1 0 0 1 1 1 7 B 4 /B
0 1 0 0 0 0 1 0 0 0 8
0 1 0 0 1 0 1 0 0 1 9
1 0 0 0 0 0 1 0 1 0 10 D 4 4 X 00 01 11 10 DD 01 11 10
D
4^3 \ 00
1 0 0 0 1 0 1 0 1 1 11 1
1 0 0 1 0 0 1 1 0 0 12 00 00
1 0 0 1 1 0 1 1 0 1 13 01 01
1 0 1 0 0 0 1 1 1 0 14
1 0 1 0 1 0 1 1 1 1 15 11 11
1 0 1 1 0 1 0 0 0 0 16
1 0 1 1 1 1 0 0 0 1 17 10 10
1 1 0 0 0 1 0 0 1 0 18
1 1 0 0 1 1 0 0 1 1 19

(a) (b)
FIGURE 6.20
Design of an 8-bit BCD-to-binary converter, (a) Truth table for a 2-digit BCD-to-binary module, (b)
K-maps plotted directly from the truth table showing minimum cover.

expressions

a = (A + B + C + D)(B + D)
b=B+CQD=B+C®D
= (B + C + D}(B + C + D)

C®D} (6.18)
= (B + C + D)(B + C + D)(B + C + D)

/ = (C + D)(A + B + D)(B + C)
g = (A + B + C)(B + C + D),