1 . Construct the truth table for a 3-input odd-parity circuit: a
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, and inverter gates in your circuit.
3. If each gate in the circuit (from question 2) has a delay
of 2 ns, what is the delay of your circuit?
4. Design a circuit which takes as input a 4-bit unsigned
integer X3X2X1X0 and
outputs a 1 if and only if X > 11. You may draw the circuit
using Logisim or by hand. (Hint: what do all the input
patterns which produce a 1 output have in common?)
5. 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.