1-Design the circuit to implement the output described in the column labeled Output-2 in the truth table in Step 1: Truth Table Construction.

2-Design a circuit using AND, OR, and NOT gates to implement the following truth table.

a b Output

0 0 0

0 1 1

1 0 1

1 1 0

This is the exclusive-OR operation, XOR. It is true if and only if a is 1 or b is 1, but not both.

3-Build a circuit using AND, OR, and NOT gates to implement the following truth table.

a b c Output

0 0 0 1

0 0 1 0

0 1 0 0

0 1 1 0

1 0 0 0

1 0 1 0

1 1 0 0

1 1 1 1

This is called a full-ON/full-OFF circuit. It is true if and only if all three of its inputs are OFF (0) or all three are ON (1).

1-Design a circuit to implement the following truth table.

a b Output

0 0 1

0 1 1

1 0 0

1 1 0

After completing the design, count how many AND, OR, and NOT gates were required to build this circuit. Now take a careful look at the truth table above and see if you can come up with a more efficient way to build the same circuit, where efficient means using fewer gates. How many gates did your efficient circuit require?

2-Assume that you are going to construct a circuit called C that has 4 inputs, a, b, c, and d, and 3 outputs, output-1, output-2, and output-3. Describe the dimensions of the truth table for circuit C.