ITPEC FE Subject A April 2024 Question 16

Topic: HardwareAlso asked in Spring 2020

Which of the following is equivalent to the circuit below?

xyzf(x,y,z)

Explanation

A single 3-input NAND gate — apply De Morgan's law to the NAND output ORed with the inverted z.

The circuit computes f = x · y + z. By De Morgan, x · y = x + y, so f = x + y + z = x · y · z: the output is 0 only when all three inputs are 1, which is a 3-input NAND.

Answer (d)

Why not others:

  • •(a) — the 3-input AND is the complement of the circuit: 1 only when all inputs are 1
  • •(b) — computes x + y · z; for x = y = z = 1 it outputs 1, but the circuit outputs 0
  • •(c) — computes x · (y + z); for x = 1, y = 1, z = 0 it outputs 0, but the circuit outputs 1

Key rule: An OR of inverted signals is a NAND of the original signals (De Morgan), so an OR fed by a NAND and inverted inputs collapses into one wider NAND.

Hardware · AI-written, may contain errors

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