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Digital Logic Design Lab Dept. of ECE

KL University, Guntur

1. Realization of gates using Universal gates

Implementation using NAND gate:

(a) NOT gate: = ′ 

 

(b) AND gate: = ∙

 

(c) OR gate: = +

 

(d) NOR gate: = ( + )′

 

(e) Ex-OR gate: = ⊕

 

A Y

0 1

1 0

A B Y

0 0 0

0 1 0

1 0 0

1 1 1

A B Y

0 0 0

0 1 1

1 0 1

1 1 1

A B Y

0 0 1

0 1 0

1 0 0

1 1 0

A B Y0 0 0

0 1 1

1 0 1

1 1 0

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Digital Logic Design Lab Dept. of ECE

KL University, Guntur

Implementation using NOR gate:

(a) NOT gate: = ′ 

 (b) AND gate: = ∙

 (c) OR gate: = +

 (d) NAND gate: = ()′

 (e) Ex-NOR gate: = ⊙ = ( ⊕ )′

 

A Y

0 1

1 0

A B Y

0 0 0

0 1 0

1 0 0

1 1 1

A B Y

0 0 0

0 1 1

1 0 1

1 1 1

A B Y0 0 1

0 1 1

1 0 1

1 1 0

A B Y

0 0 10 1 0

1 0 0

1 1 1

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Digital Logic Design Lab Dept. of ECE

KL University, Guntur

2. Combinational Logic Circuits

Half-Adder:

Half-Adder is a Combinational Logic Circuit used to perform arithmetic addition of two bits

and produces two outputs, Sum & Carry.

 

= + = ⊕  

=

Truth table

 

Half-Adder using NAND gates

Full-Adder:

Full-Adder is a Combinational Logic Circuit used to perform arithmetic addition of three bits

and produces two outputs, Sum & Carry.

 

= + + + = ⊕ Y ⊕ Z

  = + ( ⊕ Y)

Truth table

X Y S C

0 0 0 0

0 1 1 0

1 0 1 0

1 1 0 1

X Y Z S C

0 0 0 0 0

0 0 1 1 0

0 1 0 1 0

0 1 1 0 1

1 0 0 1 01 0 1 0 1

1 1 0 0 1

1 1 1 1 1

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Digital Logic Design Lab Dept. of ECE

KL University, Guntur

Full-Adder using NAND gates

Half-Subtractor:

Half-Subtractor is a Combinational Logic Circuit used to perform subtraction of two bits and

produces two outputs, Difference & Borrow

  = + = ⊕  

= ′

Truth table

 

Half-Subtractor using NAND gates

X Y D B

0 0 0 0

0 1 1 1

1 0 1 0

1 1 0 0

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Digital Logic Design Lab Dept. of ECE

KL University, Guntur

3. Code Converters

(a) Binary to Gray Code Converter:

4 bit Binary to Gray code converter is a logic circuit which converts 4 bit Binary code to

corresponding Gray code.

 

=

  = ⊕ B

  = ⊕ B

  = ⊕ B

Truth table

0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 1

0 0 1 0 0 0 1 1

0 0 1 1 0 0 1 0

0 1 0 0 0 1 1 0

0 1 0 1 0 1 1 1

0 1 1 0 0 1 0 1

0 1 1 1 0 1 0 0

1 0 0 0 1 1 0 0

1 0 0 1 1 1 0 1

1 0 1 0 1 1 1 1

1 0 1 1 1 1 1 0

1 1 0 0 1 0 1 0

1 1 0 1 1 0 1 1

1 1 1 0 1 0 0 1

1 1 1 1 1 0 0 0

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Digital Logic Design Lab Dept. of ECE

KL University, Guntur

(b) Gray to Binary Code Converter:

4 bit Gray to Binary code converter is a logic circuit which converts 4 bit Gray code tocorresponding Binary code.

=

= ⊕ G

= ⊕ G ⊕ G

= ⊕ G ⊕ G ⊕ G

Truth table

 

0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 1

0 0 1 1 0 0 1 0

0 0 1 0 0 0 1 1

0 1 1 0 0 1 0 0

0 1 1 1 0 1 0 10 1 0 1 0 1 1 0

0 1 0 0 0 1 1 1

1 1 0 0 1 0 0 0

1 1 0 1 1 0 0 1

1 1 1 1 1 0 1 0

1 1 1 0 1 0 1 1

1 0 1 0 1 1 0 0

1 0 1 1 1 1 0 1

1 0 0 1 1 1 1 01 0 0 0 1 1 1 1

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Digital Logic Design Lab Dept. of ECE

KL University, Guntur

4. Comparator

Magnitude Comparator is a logic circuit to compare the magnitude of two numbers and

contains three outputs, (A>B), (A=B) and (A<B) depending on the magnitude.

(a) One Bit Magnitude Comparator:

 

(  > ) = ′

  (  = ) = +

  (  < ) = ′

 

(b) 4 Bit Magnitude Comparator using 7485:

The 7485 is a high speed, expandable 4-bit magnitude comparator which compares

two 4-bit words and generates three outputs: (A>B), (A=B) and (A<B). Three

cascading inputs allow serial expansion over any word length without external gates.

  =    

=

For 4-bit comparison, the cascading inputs

(  > ) = 0

  (  = ) = 1

  (  < ) = 0

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Digital Logic Design Lab Dept. of ECE

KL University, Guntur

 

Function Table of 7485:

 

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Digital Logic Design Lab Dept. of ECE

KL University, Guntur

5. Multiplexer and Demultiplexer

Multiplexer:

A multiplexer is a combinational circuit that selects binary information from one of many

input lines and directs it to a single output line. The selection of a particular input line is

controlled by a set of selection lines. In general, there are 2n

input lines and n selection lines

whose bit combinations determine which input is selected.

× Multiplexer:

There are 4 input lines , , , and 2 select inputs and .

0 0

0 1

1 0

1 1

=

+ +

+

 4x1 Multiplexer

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Digital Logic Design Lab Dept. of ECE

KL University, Guntur

Demultiplexer:

A demultiplexer is a circuit that receives information on a single line and transmits this

information on one of 2n

possible output lines. The selection of a specific output line is

controlled by the bit values of n selection lines.

× :

0 0 0 0 0 0 0

0 0 1 1 0 0 0

0 1 0 0 0 0 0

0 1 1 0 1 0 0

1 0 0 0 0 0 0

1 0 1 0 0 1 0

1 1 0 0 0 0 0

1 1 1 0 0 0 1

  =

 , = , =

 , =

 1x4 Demultiplexer