Iterative circuits

Addition of two bits

As a truth table

Half adder

Two inputs (A and B) and two outputs (sum and carry). Does not take any 'previous' carry.

From universal gates

Full adder

Three inputs (A, B and previous carry) and two outputs (sum and carry). Includes carried bit from previous results
Full adder from two half adders

n-bit adder

$n$-bit adder has $2n+1$ inputs
for $n$-bit input, we have $n+1$-bit output
A K-map for big number of $n$ would be extremely huge, so the block is divided into smaller blocks