Adders are fundamental components in digital logic circuits that perform arithmetic operations, usually addition on binary numbers.
• They’re used extensively in computer processors, calculators, and other digital devices.
• It has three types: half adder, full adder and parallel n-bit adder
→ Half Adder:
A half adder is a basic digital logic circuit that adds two single binary digits (bits) together. It produces two outputs: a sum and a carry.
• It’s called a “half” adder because it doesn’t account for any carry that might result from adding multiple bits together in larger numbers.
• A half adder has two inputs: A and B, representing the two bits to be added. It generates two outputs:
Sum (S): This output represents the result of the addition of the two input bits, without considering any carry from a previous stage. The sum is calculated using an XOR gate, which outputs 1 when the number of input bits that are 1 is odd.
Carry (C): This output indicates whether there is a carry generated from adding the two input bits. The carry is calculated using an AND gate, which outputs 1 when both input bits are 1.
• Block Diagram:
• Truth Table:
• K-map:
→ Full Adder:
A full adder is a more advanced digital logic circuit compared to a half adder.
• It’s designed to add three binary inputs: two operands (A and B) and a carry input (C-in) from a previous stage.
• The full adder produces two outputs: a sum (S) and a carry output (C-out).
• Block Diagam:
• Truth Table:
• K-Map:
Logic Circuit:
Parallel n-bit Adder:
A parallel n-bit adder is a digital circuit that adds two n-bit binary numbers in parallel, meaning all corresponding bits of the two numbers are added simultaneously.
It consists of multiple full adders, one for each bit position, and produces the sum and carry outputs for each position.
Block Diagram:
Truth Table:
