Columbia University EE E3910 Elements of Digital Systems

Department of Electrical Engineering Fall 1999

Homework 2

Problem 2.9

Obtain the truth table of the following functions, and express each function in sum-of-minterms and product-of-maxterms form:

a)

b)

c)

Problem 2.12

Draw the logic diagram for the following Boolean expressions. The diagram should correspond exactly to the equation.

a)

b)

c)

Problem 2.15

Simplify the following Boolean functions, by means of a four-variable map.

a)

b)

c)

Problem 2.19

Simplify the following Boolean functions by finding all prime implicants and essential prime implicants and applying the selection rule.

a)

b)

c)

Problem 2.20

Simplify the following Boolean functions in product-of-sums form:

a)

b)

Problem 2.23

Simplify the following Boolean functions F together with the don’t care conditions d. Find all prime implicants and essential prime implicants, and apply the selection rule.

a) ,

b) ,

c) ,

Problem 2.24

Simplify the following Boolean functions F together with the don’t care conditions d in (1) sum-of-products and (2) product-of-sums form.

a) ,

b) ,