Universal Gate - NAND Digital Electronics 2.2 Intro to NAND & NOR Logic

Universal Gate – NAND

This presentation will demonstrate • The basic function of the NAND gate. • How a NAND gate can be used to replace an AND gate, an OR gate, or an INVERTER gate. • How a logic circuit implemented with AOI logic gates can Universal Gate – NAND be re-implemented using only NAND gates. • That using a single gate type, in this case NAND, will reduce the number of integrated circuits (IC) required to implement a logic circuit. Digital Electronics AOI Logic NAND Logic

2 More ICs = More $$ Less ICs = Less $$

NAND Gate NAND Gate as an Inverter Gate

X  X  X (Before Bubble)

X Z  X Y  X  Y X Z  X Y

X Y Z X Z 0 0 1 0 1 Equivalent to Inverter 0 1 1 1 0 1 0 1 1 1 0

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NAND Gate as an AND Gate NAND Gate as an OR Gate

X X Y Y X X Z  X Y  X Y Y Z  X Y  X  Y  X  Y Y NAND Gate Inverter

Inverters NAND Gate

X Y Z X Y Z 0 0 0 0 0 0 0 1 0 0 1 1 Equivalent to AND Gate Equivalent to OR Gate 1 0 0 1 0 1 1 1 1 1 1 1

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NAND Gate Equivalent to AOI Gates Process for NAND Implementation 1. If starting from a logic expression, implement the design with AOI logic. AND OR INVERTER 2. In the AOI implementation, identify and replace every AND,OR, and INVERTER gate with its NAND equivalent. 3. Redraw the circuit. 4. Identify and eliminate any double inversions (i.e., back- to-back inverters). 5. Redraw the final circuit.

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NAND Implementation NAND Implementation Solution – Step 2

Example: Identify and replace every AND,OR, and INVERTER gate with its Design a NAND Logic Circuit that is equivalent to the AOI circuit NAND equivalent. shown below.

 B C  A C

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NAND Implementation NAND Implementation Solution – Step 3 Solution – Step 4

Redraw the circuit. Identify and eliminate any double inversions.

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NAND Implementation Solution – Step 5 Proof of Equivalence

Redraw the circuit.

C B C

 B C A C

Z  B C  A C A C Z  B C  A C

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AOI vs. NAND

IC Type Gates Gate / IC # ICs IC Type Gates Gate / IC # ICs 74LS04 1 6 1 74LS00 4 4 1 74LS08 2 4 1 Total Number of ICs → 1 74LS32 1 4 1 Total Number of ICs → 3