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Sunil Thapa02721102012

BCA-II(E)

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Full SubtractorA full subtractor is a combinational circuit which is used to performsubtraction of three bits. Its has three inputs: X (Minuend),

Y (Subtrahend) and Bin(Borrow In) and two outputs: D (Difference)

and Bout(Borrow Out).

X

(Minuend)

Y(Subtrahend)

D

(Difference)

Bin(Borrow In)

Bout(Borrow Out)

Block Diagram

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A full subtractor is the combination of two half-subtractors

along with an ORgate. It has the borrow-in capability

which allows the possibility of multi-bit subtraction.

HS

1

HS

2X

Y

DBin

Bout

Full Subtractor

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Truth Table of a full-subtractor

Inputs Outputs

X Y Bin D Bout

0 0 0 0 0

0 0 1 1 1

0 1 0 1 1

0 1 1 0 11 0 0 1 0

1 0 1 0 0

1 1 0 0 0

1 1 1 1 1

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Karnaugh-Map for difference

1

XY

Bin

0

1

00 01 11 10

0 2

1

1 3

1

6 4

1

7 5

inininin BYXBYXXYBBYXD

YXYXBXYYXB inin

YXBYXB inin

inBYX

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Karnaugh-Map for borrow-out

1

XY

Bin

0

1

00 01 11 10

0 2

1 1

1 3

6 4

1

7 5

ininout YBBXYXB

).( YXBYX in

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Realization of full-subtractor

X

Y

BinD

Bout

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