# Half Adder / Full Adder / Half Subtractor / Full Subtractor:

AIM: To realize

## LEARNING OBJECTIVE:

• To realize the adder and subtractor circuits using basic gates and universal gates
• To realize a full subtractor using two half subtractors

## COMPONENTS REQUIRED:

• IC 7400
• IC 7408
• IC 7486
• IC 7432
• Patch Cords & IC Trainer Kit

## THEORY:

A combinational logic circuit that performs the addition of two data bits, A and B, is called a half-adder. Addition will result in two output bits; one of which is the sum bit,
S, and the other is the carry bit, C.

TURTH TABLE
INPUTOUTPUT
ABS = A ⊕ BC = AB
0000
0110
1010
1101

BASIC GATE

OUTPUT

The half-adder does not take the carry bit from its previous stage into account.
This carry bit from its previous stage is called carry-in bit. A combinational logic circuit that
adds two data bits, A and B, and a carry-in bit, Cin , is called a full-adder.

TURTH TABLE
INPUTOUTPUT
ABCS =A ⊕ BC = AB + BC + AC
00000
00110
01010
01101
10010
10101
11001
11111

BASIC GATE

OUTPUT

### Half Subtractor:

Subtracting a single-bit binary value B from another A (i.e. A -B ) produces
a difference bit D and a borrow out bit B-out. This operation is called half subtraction and the
circuit to realize it is called a half subtractor.

TURTH TABLE
INPUTOUTPUT
ABD = A ⊕ BB = AB
0000
0111
1010
1100

BASIC GATE

OUTPUT

HALF SUBTRACTOR USING NAND

HALF SUBTRACTOR USING NOR

### Full Subtractor:

Subtracting two single-bit binary values, B, Cin from a single-bit value A
produces a difference bit D and a borrow out Br bit. This is called full subtraction.

TURTH TABLE
INPUTOUTPUT
ABCD =A ⊕ B ⊕ CB = AB + BC + AC
00000
00110
01010
01101
10010
10101
11001
11111

BASIC GATE

OUTPUT

FULL SUBTRACTOR USING NAND

FULL SUBTRACTOR USING NOR

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