FREE LESSON · Digital logic · 2 OF 4
Binary Addition and Full Adders
Addition is a chain of local facts — Build arithmetic and see the carry path
A full adder combines three one-bit inputs.
For bits A, B, and carry-in, sum is their parity and carry-out is true when at least two inputs are true. Chaining full adders creates multi-bit addition. In a ripple-carry adder, each stage waits on the previous carry, making a simple local design into a global delay path.
Arithmetic correctness and arithmetic speed are separate design problems.
Two’s complement unifies addition and subtraction
In a fixed width, negating x means invert its bits and add one. Then subtraction x−y can use the same adder as x+(−y). Overflow is interpreted according to signed or unsigned meaning; the bit pattern alone does not carry that meaning.
Hardware manipulates patterns. The operation and type determine how those patterns should be interpreted.