Page 1050 - The Mechatronics Handbook

y y y 1
1 0
0
1
1
0
1 0 1 0 1 0 1 0
x x 00 01 11 10 (b) F (x , x , y , y ) = x x y y + x x y y
1 0
00
FACTORING GIVES F(x , x , y , y ) = (x + x )x y y
01 1 1 0 1 0 1 1 0 1 0
x (c) HENCE F(x , x , y , y ) = x y y
0 1 0 1 0 0 1 0
11 1
x
1
10 F = m 0111 + m 1111
(d) F = I
(a) y −111
0
FIGURE 36.18 Example of minimization with a K-map: (a) sample K-map, (b) expression in minterms of function
definition in (a), (c) simplification of the expression in (b), (d) simplification of the expression in (b) using single
symbol minterm and implicant notation.
y y y 1
1 0
00 01 11 10
x x m 0111
1 0
m 0101 00
I
I −101 01 1 1 −111
x 0
1 1
11
x m 1111
1
m 1101 10
y 0 F = I
−1−1
FIGURE 36.19 Example of minimization with K-map.
def d
e
e
abc 000 001 011 010 100 101 111 110
0 1 d abde
1 1 1 1 d 1 abcf
c
3 1 1
b
2 1 1 bef
4
5
a c
7 1 1
b
6 1 1
f f
F = bef + abcf + abde
FIGURE 36.20 Example of minimization with six-variable K-map.

BC B
00 01 11 10 A + C
A
B
0 0 0 0
A 1 0 0 c F = B(A + C)

FIGURE 36.21 Three-variable maxterm K-map example.

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