Page 56 - Digital Electronics by harish

Inputs Outputs
A B BORROW DIFFERENCE
0 0 0 0
0 1 1 1
1 0 0 1
1 1 0 0

DIFFERENCE = + = A ⊕ B

BORROW = B

From the truth table (A, B and DIFFERENCE), we find that an EX-OR gate can be used to
produce the DIFFERENCE. From the truth table (A, B and BORROW), we find that A‟.B
will give the BORROW. Hence, a NOT gate and an AND gate are used to produce the
BORROW.

2.5 Full subtractor

When we subtract two bits, we may get a borrow bit. Hence, a subtractor circuit needs to
subtract three bits (ie. two input bits A and B and one borrow bit C). The logic circuit which
subtracts three bits is called Full subtractor. The truth table of full subtractor is given in table.

Figure : Block diagram of full subtractor

Inputs Outputs
A B C BORROW DIFFERENCE
0 0 0 0 0
0 0 1 1 1
0 1 0 1 1
0 1 1 1 0
1 0 0 0 1
1 0 1 0 0
1 1 0 0 0
1 1 1 1 1

A full subtractor can be implemented using two half subtractors and an OR gate as shown in
the figure.

Borrow

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