Full Adder, full adder truth table
Table of Contents
Full Adder, full adder truth table, Truth Table, Implementation
The adder known as a “full adder” adds three inputs and generates two outputs. A and B make up the first two inputs, and C-IN is the third input. The normal output is designated as S, which is SUM, and the output carry is designated as C-OUT.
Eight inputs can be combined to form a byte-wide adder using full adders logic, and the carry bit can be cascaded from one adder to the next. We use a full adders because a 1-bit half-adders cannot use a carry-in bit when one is available, so we must use another 1-bit adders. So Three operands are added by a 1-bit full adder, which produces 2-bit results.
Full Adder Truth Table
Logical Expression for SUM:
A’ B’ C-IN + A’ B C-IN’ + A B’ C-IN’ + A B C-IN = C-IN (A’ B’ + A B) + C-IN’ (A’ B + A B’) = C-IN XOR (A XOR B) = (1,2,4,7)
Logical Expression for C-OUT:
A’ B C-IN + A B’ C-IN + A B C-IN’ + A B C-IN = A B + B C-IN + A C-IN = (3,5,6,7)
Another form in which C-OUT can be implemented:
A B + A C-IN + B C-IN (A + A’) = A B C-IN + A B + A C-IN + A’ B C-IN = A B (1 +C-IN) + A C-IN + A’ B C-IN = A B + A C-IN + A’ B C-IN = A B + A C-IN (B + B’) + A’ B C-IN = A B C-IN + A B + A B’ C-IN + A’ B C-IN = A B (C-IN + 1) + A B’ C-IN + A’ B C-IN = A B + A B’ C-IN + A’ B C-IN = AB + C-IN (A’ B + A B’)
Therefore COUT = AB + C-IN (A EX – OR B)
Full Adder logic circuit
Implementation of Full Adder using Half Adders
2 Half Adders and an OR gate is required to implement a Full Adder.
So Two bits can be added using this logic circuit, which sends a carry to the next higher order of magnitude and takes a carry from the next lower order of magnitude.
Implementation of Full Adder using NAND gates
Implementation of Full Adder using NOR gates
Total 9 NOR gates are required to implement a Full Adder.
So One would recognize the logic expressions of a 1-bit half-adder in the logic expression above. Two 1-bit half adders can be cascaded to create a 1-bit full adder.