Aim : Implement(i)half adder(ii) full adder using AND–OR gates.
Apparatus :
Theory :
Adder : In electronics an adder is digital circuit that perform addition of numbers. In modern computer adder reside in the arithmetic logic unit (ALU).
Binary addition is similar to that of decimal addition. Add the first digits of a number and if the count exceeds binary 2, then carry ‘1’ to the next row. Some basic binary additions are shown below.
The adder that performs simple binary addition must have two inputs (augend and addend) and two outputs (sum and carry). The device which performs above task is called a Half Adder. A Full Adder is another circuit which can add three numbers (two bits from the numbers and one carry bit from previous sum).
Half Adder
Half adder is a combinational circuit that performs simple addition of two single bit binary numbers and produces a 2-bit number. The LSB of the result is the Sum (usually represented as Sum or S0 or ∑0) and the MSB is the Carry (usually represented as COUT).
The block diagram of a half adder is shown below.
Here, ‘A’ and ‘B’ represents the input two bits that must be added and outputs are ‘Sum’ and ‘Carry’.
Half Adder Truth Table
If we assume A and B as the two bits whose addition is to be performed, a truth table for half adder with A, B as inputs and Sum, Carry as outputs can be tabulated as follows.
We can derive the Boolean Expression of Sum as follows:
Sum = A’B + AB’ = A ⊕ B
Carry = A.B
If A and B are binary inputs to the half adder, then the logic function to calculate sum S is Ex – OR of A and B and logic function to calculate carry C is AND of A and B. Combining these two, the logical circuit to implement the combinational circuit of Half Adder is shown below.
Full Adder
A Full Adder is a Combinational Logic Circuit which performs binary addition on two-digit numbers. Full adders are complex and difficult to implement when compared to half adders.
Full adder is a digital circuit used to calculate the sum of three binary bits, which is the main difference between this and half adder. Two of the three bits are same as before which are A, the augends bit and B, the addend bit. The additional third bit is carry bit from the previous stage and is called Carry–in, generally represented by CIN. It calculates the sum of three bits along including the carry. The output carry is called Carry–out and is represented by COUT.
The block diagram of a full adder with A, B and CIN as inputs and S, COUT as outputs is shown below
Full Adder Truth Table
The truth table for full adder is shown below.
|
INPUT |
OUTPUT |
|||
|
A |
B |
CIN |
Sum |
COUT |
|
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 |
Based on the truth table, the Boolean functions for Sum (S) and Carry–out (COUT) can be derived.
Cout = (A ⋅ B) + (Cin ⋅ (A ⊕ B)).
Logic diagram
PROCEDURE:
I. Place the breadboard gently on the observation table.
II. Fix the IC which is under observation between the half shadow line of breadboard, so there is no shortage of voltage.
III. Connect the wire to the main voltage source (Vcc) whose other end is connected to last pin of the IC (14 place from the notch).
IV. Connect the ground of IC to the ground terminal provided on the digital lab kit.
V. Give the input at any one of the gate of the ICs i.e. 1st, 2nd, 3rd, 4th gate by using connecting wires.
VI. Connect output pins to the led on digital lab kit.
VII. Switch on the power supply.
BY: HARDEEP KUMAR
0 Comments