digital design - sanjay vidhyadharan – sanjay vidhyadharan

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Lecture 7: Logic Gate Realization and Design

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Digital Design

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Shreya Guda 2019A7PS1202H

Eva Tiwari 2018B5A70816H

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NAND-NOR Implementations

NAND gate and NOR gates are called Universal gates

Any logic can be implemented using NAND/NOR gates

In CMOS NAND and NOR gates are basic gates

AND gate is realized by using NAND gate with Inverter

OR gate is realized by using NOR gate with Inverter

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NAND-NOR Implementations

Implementation of NAND Gate

A

B

A’

B’

(A’B’)’

= (A’)’ + (B’)’

= A + B

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NAND-NOR Implementations

Implementation of NOR Gate

A

B

A’

B’

(A’ + B’)’

= (A’)’ . (B’)’

= A . B

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NAND Implementations

NAND gate realization AB + BCA

B

B

C

Replace each gate by itscorresponding NAND realization

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NAND Implementations

NAND gate realization AB + BCA

B

B

C

Two representations of NAND gate

Bubbles indicate invert operation

(A’ + B’)

(A .B)’

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NAND ImplementationNAND gate realization AB + BCA

B

B

C

Replace all

After replacing check if all bubbles are canceling out

If not then add inverter gates to compensate bubbles

Replace all gates by NAND gates

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NAND Implementation

NAND gate realization AB + BCA

B

B

C

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NAND Implementation

NAND gate realization A(CD+B) + BC’C

D

BABC’

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NAND Implementation

NAND gate realization A(CD+B) + BC’C

D

BAB

C’

B’

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NAND Implementation

NAND gate realization A(CD+B) + BC’C

D

BAB

C’

B’

C

D

AB

C’

B’

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NAND Implementation

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NOR ImplementationF = ( A + B ) ( C + D) )

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NOR Implementation

The Gray Code

Imp. Features:

1. Only one bit ever changes between twosuccessive numbers in the sequence.

unit distance code2. It is a non-weighted code.

not suitable for arithmetic operations.

3. Gray code is a reflective code.i.e., the n-1 least significant bits for 2n-1

through 2n -1 are the mirror images of those for 0through 2n-1 -1.Binary to Gray conversion:

Gn = Bn

Gn-1 = Bn + Bn-1

Gn-2 = Bn-1 + Bn-2

.

.

.G1 = B2 + B1

Gray to binary conversion:

Bn = Gn

Bn-1 = Bn + Gn-1

Bn-2 = Bn-1 + Gn-2

.

.

.B1 = B2 + G1

Where + symbol stands for Ex- OR operation.

Example: Convert the binary 1001 to the gray code.

+ + + Binary 1 0 0 1Gray 1 1 0 1

Gray to Binary conversionGray 1 1 0 1

+ + +Binary 1 0 0 1

Gray code Reflective - code

Gray Code Decimal Binary

1- bit 2-bit 3-bit 4-bit 4-bit

01

00011110

000001011010110111101100

00000001001100100110011101010100

01234567

00000001001000110100010101100111

11001101111111101010101110011000

89

101112131415

10001001101010111100110111101111

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5-Variable k-Map

Next ClassQuine-McCluskey (QM) Technique

Reading Assignment

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Thank You