LAB REPORT (FULL ADDER ) digital logic and design

 

LAB REPORT (FULL ADDER)

COURSE TITLE:                 

                                                          DIGITAL AND LOGIC DESGION

                                          

              =

 

 

INTRODUCTION to Full Adder circuit:

A Full Adder circuit is central most digital circuit that perform addition or subtraction.

It adds together two binary digits, plus a carry-in digit to produce a sum and carry-out digit.

This is a combinational circuit which is used to add three bits is called Full Adder Circuit.

It has three inputs such as x,y and z while have two outputs i.e Sum And Carry.

TRUTH TABLE:

x	y	z	sum	carry
0	0	0	0	0
0	0	1	1	0
0	1	0	1	0
0	1	1	0	1
1	0	0	1	0
1	0	1	0	1
1	1	0	0	1
1	1	1	1	1

Equation of sum: x’y’z’+x’yz’+xy’z’xyz=(x*y)*z

Equation of carry: xy+xz+yz=x*y+(x*y)*z

 

CARRY=(X*Y) *Z+X*Y

X*Y

SUM=(X*Y) *Z

(X*Y)*Z

(X*Y)

CIRCUIT DIAGRAM:

 

HYPOTHESIS:

 The main purpose of doing this experiment

Is to add three inputs x,y and z. For experiment of different types of logic gates. We can find outputs in the form of sum and carry . We can perform Binary Addition of three inputs and two outputs.

From truth table it is clear that when all the three inputs are ON then Sum and Carry both will be 1 . x’ represent 0 and

simple x represents 1. Similarly y and z represent 1 while y’ and z’ represent 0.We will performed this experiment by

using logic gates like Exclusive OR gate, AND gate and OR gate.

EQUIPMENTS:

1)   Electronic workbench

2)   EX.OR (3)     

7486

3)   AND gate (2)

4)   7408

5)    OR gate

6)   switches (3)

7)   LEDs (2)

8)   ground

9)   +vcc  

PROCEDURE:

ü There are following steps in this experiment:

•         First draw the truth table of full adder circuit .

•         Then Write the Equations of both Sum and carry.

•         Then reduced these expressions by using Boolean Algebra.

•         After take voltage source +Vcc And Three Switches named like that x,y and z.

•         Connect one end of each switch with voltage source.

ü Other end of each switch connects with ground.

•         Perform the XOR operation of input x and y.

•         Perform the XOR operation of the outcome with carry i.e“z” .So, the sum is (x XOR y) XOR z which is also

ü represented as:(x*y) *z

•         Perform the 'AND' operation of input x and y.

•         Perform the XOR operation of input x and y.And then perform AND operation of its output with z.

•         Perform th e 'OR' operations of both the outputs that come from the previous two steps. So, the 'Carry' can be represented as:

               x*y + (x*y) *z

 

 

RESULTS & DISCUSSION:

We have get different results from the doing  of Logic gates. There Are some conditions in which one LED

is ON while other LED is OFF. It depends upon the result which is shown above in the truth table. The condition in

which carry is One that means LED connected with Carry Will be ON and similarly when sum is one in the truth

table that means LED connected with Sum will be ON.

In initial stage when all the inputs are turned OFF i.e no voltage voltage across inputs then both of the outputs i.e sum and carry will be OFF

ü But when we ON the “z “input but still OFF the x and y then resulting sum will be equa l to 1 but in this condition, carry will be 0.

ü In another condition in which all the inputs are turned ON then outputs sum and carry will also be 1.

ü In this way there are many conditions in which we may get different results,