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  Subtractor

Introduction to Subtractor:

A subtractor can be designed by using similar approach like that of an adder in electronics. The process of binary subtraction is shortened below. Like with an adder, in the common case of calculations on multi-bit numbers, three bits are included in carrying out the subtraction for each bit of the difference:

The subtrahend (Yi), minuend (Xi), and borrow in from the preceding (less significant) bit order position (Bi). The outputs are the variation bit (Di) and borrow bit Bi + 1.

Di = Xi⊕Yi⊕Bi

K-map Bi (1,2,3,7)

HALF SUBTRACTOR:

The half-subtractor is a combinational circuit that is employed to carry out subtraction of two bits. It includes two inputs, X is minuend and Y is subtrahend and two outputs D is difference and B is borrowing.

2280_Half Subtractor Homework Help.jpg

Figure: logic diagram of half subtractor

TRUTH TABLE:

X      Y      D      B

0      0      0      0

0      1      1      1

1      0      1      0

1      1      0      0

FULL SUBTRACTOR:

The Full subtractor is a combinational circuit that is employed to carry out subtraction of three bits. It has three inputs, X is stand for minuend and Y is stand for subtrahend and Z is stand for subtrahend and two outputs D is stand for difference and B is stand for borrow.

The truth table for the full subtractor is expressed below.

2006_Full Subtractor Homework Help.jpg

TRUTH TABLE:

X      Y      Z     D      B

0      0      0      0      0

0      0      1      1      1

0      1      0      1      1

0      1      1      0      1

1      0      0      1      0

1      0      1      0      0

1      1      0      0      0

1      1      1      1      1

So, Logic equations are:

D = X ⊕ Y ⊕ B

515_Full Subtractor Homework Help 1.jpg

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