## CSE 370 Assignment #3

### Due: Wednesday, January 28, 2009.

Distributed: Wednesday, January 21, 2009.

1. Katz/Borriello, Contemporary Logic Design 2e, Sections 3.1 and 3.2.3 (pages 93-103,111-114)

2. Katz/Borriello, Contemporary Logic Design 2e, Sections 4.2 (pages 164-196)

### Exercises:

1. CLD2e page 149, Chapter 3, Exercise 3.17. You can assume that all literals are available.

2. Minimize the following functions using K-maps and draw the logic gate diagrams:

1. F(w,x,y,z)=Π M(1,4,5,7,13) Π D(9,14,15).
Optimize this as a sum-of-products, and then use only NAND gates (and literals) in your final diagram.

2. F(w,x,y,z)=Σ m(1,3,5,8,9,12)+Σ d(6,10,14).
Optimize this as a product-of-sums and then use only NOR gates (and literals) in your final diagram.

3. In this question you'll design circuits that divide two 2-bit binary numbers A = (A1 A0) and B=(B1 B0) and computes the 2-bit quotient Q=(Q1 Q0) of A divided by B and the remainder R=(R1 R0) of A divided by B. In the case that B is 0 the answer is undefined so the values on such inputs can be taken as don't cares.

1. Draw truth tables for Q1,Q0,R1,R0.

2. Use K-maps to minimize these in SOP form.

3. Use K-maps to minimize these in POS form.

### Rationale:

• Practice circuit design and optimization with K-maps