5. NOR Logic Synthesis

A NOR gate is a universal logic primitive. By specific arrangement, any Boolean function can be replicated:

• NOT A Output: Synthesized by tying both inputs of a NOR gate to A.
  • Output Equation: NOT(A) = NOR(A, A)
• OR Output: Synthesized by inverting the output of a NOR gate.
  • Output Equation: OR(A, B) = NOR(NOR(A, B), NOR(A, B))
• AND Output: Synthesized by inverting the individual inputs before feeding them into a NOR gate (De Morgan's Law).
  • Output Equation: AND(A, B) = NOR(NOR(A, A), NOR(B, B))

Step-by-Step Logic Evaluation:

• NOT Gate: If A is 0, NOR(0, 0) is 1. If A is 1, NOR(1, 1) is 0.
• OR Gate: The first NOR gate produces the inverse of (A OR B). The second NOR gate inverts that result, restoring the OR logic.
• AND Gate: By first inverting A (using NOR(A, A)) and B (using NOR(B, B)), and then passing these inverted signals through a final NOR gate, we implement the AND function according to De Morgan's Law: NOR(NOT A, NOT B) = (A AND B).

Circuit Implementation:

• NOT Block: Connect input A to both inputs of the first NOR gate.
• OR Block: Connect inputs A and B to the second NOR gate, then feed its output into both inputs of the third NOR gate.
• AND Block: Connect input A to the fourth NOR gate (tied inputs) and input B to the fifth NOR gate (tied inputs). Connect the outputs of these two gates to the inputs of the sixth NOR gate.
• Connect: Map the final outputs of the NOT, OR, and AND blocks to their respective destination probes.