“To design & construct Full Subtractor & To Verify its Truth Table”

“To design & construct Full Subtractor & To Verify its Truth Table”

1.     Objective:

The main objective is to design and verify the truth table of

        i.            Full Subtractor

2.     Components:

        i.            Bread Board

      ii.            Connecting Wires

    iii.            LED

    iv.            Battery

      v.            4 IC’s

a.       IC 7486 for XOR Gate

b.      IC 7408 for AND Gate

c.       IC 7432 for OR Gate

d.      IC 7404 for NOT Gate

3.     Introduction:

3.1.Bread Board:

A bread board is an electronic board into which the electrical components like diodes and resistors are placed. The sockets of bread board are sturdy and rugged. Diodes or other electrical components should be placed without making any damage to the board.

3.2.Integrated Circuits:

A circuit of transistors, resistors, and capacitors constructed on a single semiconductor wafer or chip, in which the components areinterconnected to perform a given function. IC’s consume very little current, generate comparatively little heat, and are far more shock-proof and reliable than the older discrete-component circuits.

An integrated circuit consists of a number of circuit components (e.g. transistors, diodes, resistors etc.) and them inter connections in a single small package to perform a complete electronic function. These components are formed and connected within a small chip of semiconductor material. IC’s can be used as advanced logic gates. Some IC’s description is given below which can be used for logic gates.

3.3.Light Emitting Diodes:

A light-emitting diode (LED) is a semiconductor device that emits visible light when an electric current passes through it. LED’s convert electrical energy to light energy. In electronics, polarity indicates whether a circuit component is symmetric or not. Being diodes, will only allow current to flow in one direction. And when there’s no current-flow, there’s no light. The positive side of the LED is called the “anode” and is marked by having a longer “lead,” or leg. The other, negative side of the LED is called the “cathode.” 

3.4.Full Subtractor:

Subtractor is the one which used to subtract two binary number(digit) and provides Difference and Borrow as output. In digital electronics we have two types of Subtractor.

A logic Circuit Which is used for Subtracting Three Single Bit Binary digit is known as Full Subtractor. 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 BOR_IN in the diagram below) and so allows cascading which results in the possibility of multi-bit subtraction.

4.     Circuit Diagram:

5.     Experimental Setup:

6.     Experimentation:

1.      First of all, suitable IC’s for XOR ,OR NOT and AND gate are chosen, i.e. IC 7486 ,7432 ,7404 & 7408 respectively.

2.      Inserted IC’s on the bread board.

3.      As there are 14 pins on IC, 7^th pin is grounded and a positive potential is applied to the 14^th pin via a battery of potential less than 5V.

4.      First Input A of XOR is connected with input of NOT gate and the output of NOT Gate is given to the first input of first AND gate.

5.      Second input B of XOR is connected with the second input of first AND gate.

6.      Output of first XOR is given to the first input of second XOR, while its second input is left to consider it carry .

7.      The first input of second XOR is connected to the input of second NOT Gate and its output is given to the first input of second AND gate, while second input of second XOR is connected to the second input of AND gate.

8.   First LED is inserted on bread board with its positive terminal connected to the output   of second XOR gate and negative signal is given to the other terminal.

9.      The outputs of both AND gates are given to the OR gate as its two inputs.

10.  Second LED is inserted on bread board with its positive terminal connected to the output  of OR gate and negative signal is given to the other terminal.

11.  Then one by one checked all the eight possible combination of three inputs so that truth table can be verified.

12.  Truth table is drawn.

7.     Observations & Calculations:

The truth table for Full Adder which we have observed is shown below:

A	B	Bin	D	B0
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

8.     Results & Discussion:

We have designed Full Subtractor combining two half Subtractor in a suitable way. As we have also verified the truth tables of full Subtractors we can deduce some main points from this. The total OR, XOR & AND logic gates in IC’s 7432 & 7408 respectively are 4. The whole circuit is OFF three times when all of the inputs are zero, when two are ON & one is OFF and ON when all of these are ON and when two of these are OFF..

9.     Conclusion:

Through this experiment we have designed Full Subtractor by using Half Subtractor and their truth tables are verified by using IC’s inserted on bread board along with LED to show OFF or ON status of output.

10. References:

I.                      http://logic.ly/lessons/nor-gate/

II.                    http://isweb.redwoods.edu/instruct/calderwoodd/diglogic/full.htmhttp://www.bscshortnote.com/what-is-full-adder/

III.                   http://www.ustudy.in/node/3036

IV.                   http://teahlab.com/Full_Subtractor/