© 2015 IJIRT | Volume 1 Issue 12 | ISSN: 2349-6002
Binary Subtractor Circuits
Simran Singh Oberoi ,SangeetKumar,Virenderpratap
Electrical and Electronics Engineering, Dronacharya College of Engineering, Gurgaon, India
Abstract:In this paper we would be studying about
subtractor that are used two subtract two binary
numbers. The main focus of this paper is on the
two main types of subtractors, i.e. half subtractor
and full subtractor. This paper will be mainly
focused on the two subtractors but we will also be
having a brief on other type of subtractor.
Introduction
Subtractors are usually implemented within a binary
adder for only a small cost when using the standard
two's complement notation, by providing an
addition/subtraction selector to the carry-in and to
invert
the
second
operand.
In electronics,
a subtractor can be designed using the same approach
as that of an adder. The binary subtraction process is
summarized below. As with an adder, in the general
case of calculations on multi-bit numbers,
three bitss are involved in performing the subtraction
for each bit of the difference: the minuend (
), subtrahend (
), and a borrow in from the previous
(less significant) bit order position (
are the difference bit (
). The outputs
) and
borrow bit
. The subtractor is best understood
by considering that the subtrahend and both borrow
bits have negative weights, whereas the X and D bits
are positive.
Binary Subtractor are of two types. They are
classified into:(1) Half Subtractor
(2) Full Subtractor
HALF SUBTRACTORThe half-subtractor is a combinational circuit which
is used to perform subtraction of two bits. It has two
inputs, X (minuend) and Y (subtrahend) and two
outputs D (difference) and B (borrow).An important
point worth mentioning is that the half substractor
diagram aside implements (b-a) and not (a-b) as
borrow is calculated from equation
IJIRT 101878
The half Subtractor subtracts two input bits and
generates a difference and borrow, which are the two
outputs of a half subtractor. The input variables of a
half subtractor are called the Minuend and subtrahend
bits.
 Truth table
X
Y
D
B
0
0
0
0
0
1
1
1
1
0
1
0
1
1
0
0
From the above table one can draw the Karnaugh
map for "difference" and "borrow".
So, Logic equations are:
INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY
131
© 2015 IJIRT | Volume 1 Issue 12 | ISSN: 2349-6002
FULL SUBTRACTOR
As in the case of the addition using logic gates, a full
subtractor is made by combining two half-subtractors
and an additional OR-gate. A full subtractor has the
borrow in capability (denoted as BORIN in the
diagram below) and so allows cascading which
results in the possibility of multi-bit subtraction.
Difference=A'B'C+A'BB'+AB'C'+ABC
Reduce
it
like subtractor
Then
We
got
Difference=A B C
Borrow=A'B'C+A'BC'+A'BC+ABC
=A'B'C+A'BC'+A'BC+A'BC+A'BC+ABC --------->
A'BC=A'BC+A'BC+A'BC
=A'C(B'+B)+A'B(C'+C)+BC(A'+A)
Borrow=A'C+A'B+BC
1
1
1
1
1
So, Logic equations are:
A
 Truth table
The truth table for the full subtractor is given
below.[1]
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
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REFERENCE



www.google.com
www.circuits-today.com
www.wikipedia.com
Digital Electronics By J B Gupta
INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY
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