COSC 3332 HW2

Question 1

Construct a truth table for the following:

• xyz + x(yz)' + x'(y + z) + (xyz)'
• (z + y')(x' + z')(y' + z')

Question 2

Simplify the following functional expressions using Boolean algebra and its identities. List the identity used at each step.

• F(x, y, z) = y(x' + (x + y)')
• F(x, y, z) = x'yz + xz
• F(x, y, z) = (x' + y + z')' + xy'z' + yz + xyz

Question 3

The truth table for a Boolean expression is shown below. Write the Boolean expression in sum-of-products form. see image.

Question 4

Given the function F(x, y, z) = y(x'z+xz') + x(yz + yz')

• List the truth table of F
• Draw the logic diagram using the original Boolean expression
• Simplify the expression using the Boolean algebra identities
• List the truth table for your answer in part c.
• Draw the logic diagram for the simplified expression in part c.

Question 5

Complete the truth table for the following sequential circuit: see image.