The logic gate that works as 2-bits comparator:

To add two 8-bits number we need

say you have a 3-bit even parity generator that sent the following sequence "0100" to a 4-bit even parity checker. the output of the parity checker would be...

The boolean expression of an even function is

for even parity generator, the parity bit is the output & it must be generated so that the total number of 1's is even. meaning the output of the function will equal 1 whenever the inputs have an odd number of 1's.

this is the same definition as an...

for a 2×1 mux where the inputs are x⁰, x¹, and the selection line is S.

the output F=...

In the 4bit full adder an over can be detected by connecting the carry out of the 3th adder and the carry out of the 4th adder into

A, B unsigned numbers.
A - B will generate a carry that we discard when...