LOGIC DESIGN

Homework 5

1. Minimize the following function using the K-map to 5 terms, 14 literals.

f(a,b,c,d) = ∑m(0, 5, 6, 7, 8, 10, 11, 12, 13, 14)

Minimized function: f() =

2. Minimize the following function using the K-map to 5 terms, 14 literals.

f(a,b,c,d) = ∑m(0, 1, 2, 5, 7, 8, 9, 11, 12, 15)

Minimized function: f() =

3. Minimize the following functions:

1. f(a,b,c,d) = c’d + abc’ + abd’ + a’b’d

2. f(x,y,z)= wy + yz + xy’z

3. f(w,x,y,z) = wyz + w’x’ + wxz’

4. Design a digital circuit with three inputs x, y, z and three outputs A, B, C

When the binary input is 0, 1, 2, or 3, the binary output is one greater than the input. When the binary

input is 4, 5,6, or 7 the binary output is two less than the input.

5. Design a four bit circuit 2’s complementer. (The output is the 2’s complement of the input).