4. NAND Logic Synthesis

A NAND 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 NAND gate to A.
  • Output Equation: NOT(A) = NAND(A, A)
• AND Output: Synthesized by inverting the output of a NAND gate.
  • Output Equation: AND(A, B) = NAND(NAND(A, B), NAND(A, B))
• OR Output: Synthesized by inverting the individual inputs before feeding them into a NAND gate (De Morgan's Law).
  • Output Equation: OR(A, B) = NAND(NAND(A, A), NAND(B, B))

Step-by-Step Logic Evaluation:

• NOT Gate: If A is 0, NAND(0, 0) is 1. If A is 1, NAND(1, 1) is 0.
• AND Gate: The first NAND gate produces the inverse of (A AND B). The second NAND gate inverts that result, restoring the AND logic.
• OR Gate: By first inverting A (using NAND(A, A)) and B (using NAND(B, B)), and then passing these inverted signals through a final NAND gate, we implement the OR function according to De Morgan's Law: NAND(NOT A, NOT B) = (A OR B).

Circuit Implementation:

• NOT Block: Connect input A to both inputs of the first NAND gate.
• AND Block: Connect inputs A and B to the second NAND gate, then feed its output into both inputs of the third NAND gate.
• OR Block: Connect input A to the fourth NAND gate (tied inputs) and input B to the fifth NAND gate (tied inputs). Connect the outputs of these two gates to the inputs of the sixth NAND gate.

Connect: Map the final outputs of the NOT, AND, and OR blocks to their respective destination probes.