Homework #2

1. Simplify the following Boolean expressions using a K map.

a) f(x,y.z) = xy + x’y’z’ + x’yz’

b) f(w,x,y,z) = wxy + x’z’ + w’xz

c) f(a,b,c,d) = ab + bcd’ + ab’c’d’

d) f(a,b,c,d) = Σ(1,4,5,6,12,14,15)

e) f(r,s,u,v) = П(1,4,5,6,12,14,15)

2. Design an exclusive-or gate using only NAND gates.

3. Design a BCD to seven segment decoder. You do not need to draw the circuit.

a

b f

8 = g

c e

d

a

b f

0 =

c e

d

b

1 =

c

a

f

2 = g

c

d

a

f

3 = g

e

d

b f

4 = g

e

a

b

5 = g

e

d

a

b

6 = g

c e

d

a

f

7 =

e

a

b f

9 = g

e