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Home Electrical and Electronics Digital Circuit System To verify the truth table of half adder and full adder
Digital Circuit System Lab Experiments

To verify the truth table of half adder and full adder



Aim

To verify the truth table of half adder and full adder.

Apparatus Required:

Digital trainer kit, IC 7486, IC 7432, IC 7408, Connecting wires.

Theory

Adder circuit is a combinational digital circuit that is used for adding two numbers. A typical adder circuit produces a sum bit (denoted by S) and a carry bit (denoted by C) as the output. Adder circuits can be used for a lot of other applications in digital electronics like address decoding, table index calculation etc. Adder circuits are of two types: Half adder ad Full adder

Half adder

A half adder is a combinational circuit that performs the sum of two binary digits (A, B) to givea maximum of two binary outputs namely the sum(S) and the carry(C). Carry is the higher order bitand the sum is the lower order bit of the output. Functional Table of the Half-Adder is given below

Functional Table of Half Adder

A B Sum Carry
0 0 0 0
0 1 1 0
1 0 1 0
1 1 0 1

half-adder-block-diagram

The Boolean expression for the sum (S) and carry(C) of half adder is,

Sum = AB' + A'B = A⊕B

Carry= A.B

Full adder

A full adder is a combinational circuit that performs the sum of three binary digits (A, B, Cin) to give a maximum of two binary outputs namely the sum(S) and the carry- out (Cout).The full adder becomes necessary when a carry input must be added to the two binary digits to obtain the correct sum. A half adder has no input for carries from previous circuits

Functional Table of Full Adder

A B C 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

full-adder-block-diagram

The Boolean expression for the sum (S) and carry-out (Cout) of full adder is,

Sum = A'B'C + A'BC' + AB'C' + ABC

Cout = A'BC + AB'C + ABC' + ABC

Simplification of Logic Equations

Sum = A'B'C + A'BC' + AB'C' + ABC

= A’(B’C+BC’) + A(B’C’+BC)

=A⊕B⊕C

Cout = A'BC + AB'C + ABC' +ABC

= A'BC + ABC+ AB'C +ABC'

= AB(C+C’) + C(A’B+AB’)

=AB + C(A⊕B)

half&full-adder-logic-diagram

The full adder drawn above can be visualized as a combination of two half adders. It uses two XOR gates, the output of 1st XOR gate (i.e. Sum A+B) is taken as input to 2nd XOR gate and the other is the third input( usually the Cin), the outputs of the AND gates which are nothing but the carry of HA are ORed together. The FA drawn as a combination of two HA is shown below.

full-adder-using-two-ha

Procedure:-

  1. Place the breadboard gently on the observationtable.
  2. Fix the IC which is under observation between the half shadow lineof breadboard, so there is no shortage ofvoltage.
  3. Connect the wire to the main voltage source (Vcc) whose other end is connected to last pin of the IC (14 place from thenotch).
  4. Connect the ground of IC (7th place from the notch) to the ground terminal provided on the digital labkit.
  5. Give the input at the gate of the ICs by using connecting wires. (In accordance to IC provided).
  6. Connect output pins to the led on digital lab kit.
  7. Switch on the powersupply.
  8. If led glows then output is true, if it doesn’t glow output is false, which is numerically denoted as 1 and 0respectively.
  9. Verify the truthtable

Precautions:

  1. All ICs should be checked before starting theexperiment.
  2. All the connection should betight.
  3. Always connect ground first and then connectVcc.
  4. Suitable type wire should be used for different types ofcircuit.
  5. The kit should be off before changing theconnections
  6. after the completion of experiment, switch off the supply of theapparatus.

Result:The truth table of half adder and full adder is verified.

Questions:

Q1:What is a combinationalcircuit?

Ans:In a combinational circuit, the output depends upon present input(s) only i.e, not dependant on the previous input(s). The combinational circuit has no memory element. It consists of logic gates only

Q2:What is ahalf-adder?

Ans:A logic circuit, that can add two 1-bit numbers and produce outputs for sum and carry, is called a half-adder.

Q3:What is afull-adder?

Ans:A binary adder, which can add two 1-bit binary numbers along with a carry bit and produces outputs for sum and carry is called a full-adder.












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