digital design - sanjay vidhyadharan – sanjay vidhyadharan
TRANSCRIPT
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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