1 . Construct the truth table for a 3-input odd-parity circuit: a
circuit
with three inputs and one output, where the output is 1 if and only if
an odd number of the inputs are 1.

2. Using Logisim, design and draw a schematic of a 3-input
odd-parity circuit. You may use AND,
NAND, OR, NOR, exclusive-OR, and inverter gates in your circuit.

3. DeMorgan's Theorem (text, In More Depth 14-1)

not ( and ( x , y ) ) = or ( not ( x ),
not ( y ) )

not ( or ( x, y ) ) = and ( not ( x ), not ( y ) )

Prove DeMorgan's Theorem by setting up a truth table of the form

not ( or ( x, y ) ) = and ( not ( x ), not ( y ) )

Prove DeMorgan's Theorem by setting up a truth table of the form

x |
y |
not(x) |
not(y) |
not ( and ( x , y ) ) | or ( not ( x ), not ( y ) ) | not ( or ( x, y ) ) | and ( not ( x ), not ( y ) ) |

0 |
0 |
||||||

0 |
1 |
||||||

1 |
0 |
||||||

1 |
1 |

4. Prove that the NOR gate is universal by showing how to build the AND, OR, and NOT functions using a two-input NOR gate.

Hint: first build an inverter from a NOR gate. Then use inverters and NOR gates to construct an OR gate and to construct an AND gate. You will need DeMorgan's theorem to build the AND gate.