## Monday, April 4, 2011

### IMPLEMENTATION OF HALF SUBTRACTOR & FULL SUBTRACTOR

IMPLEMENTATION OF HALF SUBTRACTOR & FULL SUBTRACTOR

AIM:

To design and verify the truth table of the Half Subtractor & Full Subtractor circuits.

APPARATUS REQUIRED:

 S.No Name of the Apparatus Range Quantity 1. Digital IC trainer kit 1 2. AND gate IC 7408 3. OR gate IC 7432 4. NOT gate IC 7404 5. EX-OR gate IC 7486 6. Connecting wires As required

THEORY:

The arithmetic operation, subtraction of two binary digits has four possible elementary operations, namely,

0 - 0 = 0
0 - 1 = 1 with 1 borrow
1 - 0 = 1
1 - 1 = 0

In all operations, each subtrahend bit is subtracted from the minuend bit.  In case of the second operation the minuend bit is smaller than the subtrahend bit, hence 1 is borrowed.

HALF SUBTRACTOR:

A combinational circuit which performs the subtraction of two bits is called half subtractor.  The input variables designate the minuend and the subtrahend bit, whereas the output variables produce the difference and borrow bits.

FULL SUBTRACTOR:

A combinational circuit which performs the subtraction of three input bits is called full subtractor.  The three input bits include two significant bits and a previous borrow bit.  A full subtractor circuit can be implemented with two half subtractors and one OR gate.

HALF SUBTRACTOR

TRUTH TABLE:

 S.No INPUT OUTPUT A B DIFF BORR 1. 0 0 0 0 2. 0 1 1 1 3. 1 0 1 0 4. 1 1 0 0

DESIGN:

From the truth table the expression for difference and borrow bits of the output can be obtained as,

Difference, DIFF = A  B
Borrow, BORR = A’ . B

CIRCUIT DIAGRAM:

FULL SUBTRACTOR
TRUTH TABLE:

 S.No INPUT OUTPUT A B C DIFF BORR 1. 0 0 0 0 0 2. 0 0 1 1 1 3. 0 1 0 1 1 4. 0 1 1 0 1 5. 1 0 0 1 0 6. 1 0 1 0 0 7. 1 1 0 0 0 8. 1 1 1 1 1

DESIGN:

From the truth table the expression for difference and borrow bits of the output can be obtained as,

Difference, DIFF= A’B’C + A’BC’ + AB’C’ + ABC
Borrow, BORR = A’BC + AB’C + ABC’ +ABC

Using Karnaugh maps the reduced expression for the output bits can be obtained as,

DIFFERENCE

DIFF = A’B’C + A’BC’ + AB’C’ + ABC = A  B  C

BORROW

BORR = A’B + A’C + BC

CIRCUIT DIAGRAM:

PROCEDURE:

1. Connections are given as per the circuit diagrams.
2. For all the ICs 7th  pin is grounded and 14th pin is given +5 V supply.
3. Apply the inputs and verify the truth table for the half subtractor and full subtractor circuits.

RESULT:

The design of the half subtractor and full subtractor circuits was done and their truth tables were verified.

Vijitha Jeya said...

really itz useful....but we need logic circuit for bot half and full subtractor

Rana Usman said...

usefull

branchtoppers.com said...

requires details description of circuit diagrams

Sowmya L said...

thank you very much...!