Lecture_10...2013

Pertemuan 8
Digital Electronics

ADDER

(Lecture #10)

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ECE 301 - Digital Electronics

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The Half Adder (HA)

Single-bit Adder Circuits

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ECE 301 - Digital Electronics

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Binary Addition

00 11

+ 0 +1 + 0 +1

01 1 10

Sum

Carry

Sum

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ECE 301 - Digital Electronics

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The Half Adder

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ECE 301 - Digital Electronics

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The Half Adder

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ECE 301 - Digital Electronics

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The Full Adder (FA)

Single-bit Adder Circuits

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ECE 301 - Digital Electronics

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Binary Addition

00 00

0011

+ 0 +1 + 0 +1

01 1 10

Carry-out

Sum

11 11

0011

+ 0 +1 + 0 +1

1 10 10 11

Carry-in

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ECE 301 - Digital Electronics

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The Full Adder

Cin

Cout

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ECE 301 - Digital Electronics

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The Full Adder

S = X xor Y xor Cin

Cout = X.Y + X.Cin + Y.Cin

Cin

Cin

Cin

Cin

S

Cout

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ECE 301 - Digital Electronics

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The Full Adder

X

Y

Cin

S

Cout

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ECE 301 - Digital Electronics

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The Full Adder

Half Adder

Half Adder

Cin

Cin

Cin

Cin + xy

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ECE 301 - Digital Electronics

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Multi-bit Adder Circuits

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ECE 301 - Digital Electronics

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Implementations of Multi-bit Adders:

1. Ripple Carry Adder

2. Carry Lookahead Adder

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ECE 301 - Digital Electronics

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Ripple Carry Adder

Multi-bit Adder Circuits

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ECE 301 - Digital Electronics

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Ripple Carry Adder

1

0

1

0

1

0

0

1

+

1

Carry-in

0

1

0

0

1

Carry-out

1

1

Carry ripples from one column to the next

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ECE 301 - Digital Electronics

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Ripple Carry Adder

Carry ripples from one stage to the next

Carry-in

Carry-out

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ECE 301 - Digital Electronics

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Ripple Carry Adder

n-bit Ripple Carry Adder

Composed of n 1-bit Full Adders

Carries ripple from LSB stage to MSB stage

Delay ~ (n)*(delay of single FA stage)

Area required is linear in n

4-bit Ripple Carry Adder

Composed of 4 1-bit Full Adders

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ECE 301 - Digital Electronics

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The Ripple Carry Adder is slow!

Why?

How can the speed of the adder be increased?

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ECE 301 - Digital Electronics

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Increasing the speed of the Adder

Method A: Include all inputs and outputs in the design

Inputs = Xi, Yi, Cin,i; Outputs = Si, Cout,i

1-bit3 inputs2 outputs

2-bit5 inputs3 outputs

4-bit9 inputs5 outputs

n-bit2n+1 inputsn+1 outputs

Large number of operands, but only 2 logic levels

Increase in speed

Increase in area required

decrease propagation delay

increase # of logic gates

Use Truth Table

and K-Map to

derive logic functions

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ECE 301 - Digital Electronics

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Increasing the speed of the Adder

Method B: Manipulate the Boolean Algebra

(results in the design of the Carry Lookahead Adder)

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ECE 301 - Digital Electronics

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Carry Lookahead Adder

Multi-bit Adder Circuits

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