# Universal Gates

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28-Apr-2015Category

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Universal Gate NANDDigital Electronics

Universal Gate NANDThis 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 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.AOI Logic NAND Logic

2

More ICs = More $$

Less ICs = Less $$

NAND GateX Y

Z XYXY

X 0 0

Y 0 1

Z 1 1

11

01

10

3

NAND Gate as an Inverter GateX X XX(Before Bubble)

ZX

X 0 1

Z 1 0Equivalent to Inverter

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NAND Gate as an AND GateXYX YNAND Gate Inverter

ZXYXY

X Y 0 0 1 1 0 1 0 1

Z 0 0 0 15 Equivalent to AND Gate

NAND Gate as an OR GateXX YNAND Gate

YZ XY XY XY

Inverters

X Y 0 0 1 1 0 1 0 1

Z 0 1 1 16 Equivalent to OR Gate

NAND Gate Equivalent to AOI GatesAND OR INVERTER

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Process for NAND Implementation1. If starting from a logic expression, implement the design with AOI logic. 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., backto-back inverters).

5. Redraw the final circuit.

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NAND ImplementationExample: Design a NAND Logic Circuit that is equivalent to the AOI circuit shown below.

BC A C

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NAND ImplementationSolution Step 2

Identify and replace every AND,OR, and INVERTER gate with its NAND equivalent.

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NAND ImplementationSolution Step 3

Redraw the circuit.

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NAND ImplementationSolution Step 4

Identify and eliminate any double inversions.

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NAND ImplementationSolution Step 5

Redraw the circuit.

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Proof of Equivalence

C

BC

BCAC

AC

Z BCAC Z BC AC14

AOI vs. NAND

IC Type 74LS04 74LS08 74LS32

Gates 1 2 1

Gate / IC 6 4 4

# ICs 1 1 1 3

IC Type 74LS00

Gates 4

Gate / IC 4

# ICs 1 1

Total Number of ICs

Total Number of ICs

15

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