Objectives: Learn how to represent hardware combinational logic in truth tables, logic equations, and logic blocks composed of gates, how to minimize logic using a Karnaugh map and laws of Boolean algebra. Write your answers on this sheet and submit the document through the Blackboard portal for this assignment.

1. Design a circuit that takes three bits (X2, X1, X0) as input and produces one bit (O) as output. O is 1 if and only if the number of ones in X2, X1, and X0 is one or fewer.

(a) Complete the following truth table.

(b) Write the sum-of-product form for the output O without any simplification.

(c) Simplify the equation using a Karnaugh map. (20 points)

(d) Draw the logic block that directly implements this function using only NOT, AND, and OR gates. (20 points)

2. Examine the following logic block.

(a) Write the logic equation that represents this logic block.

(b) Simplify the logic equation using the laws of boolean algebra and DeMorgans theorems to minimize the number of terms and boolean operations. Indicate which law or theorem is applied at each step.

Inputs X2 | X| | XO Output