1. Given the truth table shown below, derive the sum-of-products boolean expression (unsimplified) representing the output Q.

x y z Q

0 0 0 1

0 0 1 0

0 1 0 0

0 1 1 1

1 0 0 0

1 0 1 0

1 1 0 0

1 1 1 1

A. x'y'z' + x'yz + xyz

B. xyz + xyz + xyz

C. (x'y'z' )(x'yz)(xyz)

D. (x+y+z)(x+y'+z')(x'+y'+z')

2. Given the truth table shown below, derive the product-of-sums boolean expression (unsimplified) representing the output Q.

x y z Q

0 0 0 1

0 0 1 0

0 1 0 0

0 1 1 1

1 0 0 1

1 0 1 1

1 1 0 1

1 1 1 1

A. (x'y'+z)(x'y+z')

B. (x'+y'+z)(x'+y+z')

C. (x+y+z')(x+y'+z)

D. (x'y'z)(x'yz')