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1、学习必备欢迎下载Chapter 1 1. x yzx + y y + z (x + y )(y + z)xyxzy z xy + xz + y z0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 1 2. a) w x yzwxxzy wx + xz + y b) w x yzw + x + y + z0 0 0 0 0 0 1 1
2、 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 0 1 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 1 0 1 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 1 0 0 1 1 1 0 0 1 1 1 0 1 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 1 0 1 1 1 1 1
3、 0 0 1 0 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 c) w x yzw x yz w xyz w x yz w xyz w x yz + w xyz + w x yz + w xyz 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 1 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 1 1
4、1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 学习必备欢迎下载3. abab(ab) a b a + baba + b (a + b) a b a b0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 0 1 0 0 1 0 1 1 1 0 1 0 0 1 0 1 1 1 0
5、0 0 0 1 1 1 0 0 0 0 4. a) w + x + y + z b)w + x + yzc)(w + x) + (w + y) + (w + z) + (x + y) + (x + z) + (y + z) = w + x + y + z5. a) wx yz 00 01 11 10 b) wx yz 00 01 11 10 00 1 1 0 0 00 1 1 0 1 01 0 1 1 0 01 1 1 1 0 11 0 0 1 1 11 1 1 1 0 10 1 0 0 1 10 1 0 0 1 w x y + w xz + wxy + wx zx z + w y + xz
6、+ xy or or x y z + w y z + xyz + wyzx z + w y + xz + y z6. a) wx yz 00 01 11 10 b) wx yz 00 01 11 10 00 1 0 0 1 00 X 1 1 X 01 1 X 1 1 01 0 X X 0 11 0 1 X 0 11 0 0 X 0 10 0 X X 0 10 X X X X w z + xyx7. a) wx yz 00 01 11 10 b) wx yz 00 01 11 10 c) wx yz 00 01 11 10 00 0 1 0 0 00 1 0 0 0 00 0 1 0 1 01
7、0 1 1 0 01 1 1 0 0 01 1 0 1 0 11 1 1 1 1 11 1 1 0 1 11 0 1 0 1 10 0 0 0 0 10 1 0 0 1 10 1 0 1 0 wx + xz + w y zy z + xy + wzAlready minimal8. a) b) c) 9. wxy + wxz + w xy + xyz :wx yz 00 01 11 10 00 0 0 0 0 01 0 0 1 1 11 1 1 1 1 10 0 0 0 0 wx + xy 学习必备欢迎下载10. a) b) 11. Change the AND gates to NAND g
8、ates. The rest of the circuit is unchanged.12. Remove the tri-state buffers and do one of the following: a)Change each 2-input AND gate to a 3-input AND gate. Each gates inputs should be its two original inputs and E, or b)Have each AND gates output serve as an input to another 2-input AND gate, one
9、 gate for each original AND gate. The second input to the new 2-input AND gates is E. 13. 14. 学习必备欢迎下载15.Set up Karnaugh maps for each output, then develop minimal logic expressions and design the appropriate logic circuits.X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1
10、X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X
11、 = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y)
12、= X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0
13、Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 +
14、 X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y
15、1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 +
16、X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1
17、Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X
18、1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y
19、0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X
20、1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X
21、0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X
22、 Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1
23、X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y0
24、00 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01
25、11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10
26、X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:
27、X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1
28、Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 0
29、1 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 1
30、0 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y)
31、 = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y: X1X0Y1Y000 01 11 10 X = Y:X1X0Y1Y000 01 11 10 X Y) = X1Y1 + X0Y1Y0 + X1X0Y0(X = Y) = X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 + X1X0Y1Y0 = (X1Y1)(X0Y0)(X Y) = X1Y1 + X1X0Y0 + X0Y1Y016. C3 = X2Y2 + ( X2Y2)(X1Y1 + (X1Y1)(X0Y0 + (X0Y0)C0) C4 = X3Y3 + ( X3Y3)(X2Y2 + (X2Y2)(X1Y1 + (X1Y1)(X0Y0 + (X0Y0)C0)17.