In this adder we have 2 inputs of N-bit numbers and one output of N-bit number with a carry. We can achieve this either using

**Serial addition or****Parallel addition**

**Serial adder:**

This is the one which would accept bit by bit input of the n-bit numbers and there is a bit by bit output of the n-bit Sum. In this adder we would be required one full adder and a memory element.

Hence we see we require lesser hardware. The circuit for serial addition is as follow:

**Parallel adder:**

Parallel adder is the one where we input the all the bits of two given numbers and we don’t need any memory element.

**Carry propagate adder (CPA) or Ripple carry adder: **In this adder we need n full adders for n bit adder. In this adder we use the n full adders in cascaded from to implement the ripple carry adder. This type of adder is also called carry propagation adder. The circuit for 4-bit parallel adder is as follow:

Let’s now calculate the time required for the carry to propagate from adder 1 to last adder and when we get the final result.

If at time t=0 we input the variables, we’ll the carry of 1st adder at t=2Δ which would be propagated to 2nd adder and at t=3Δ we get the sum variable S1. When at t=2Δ carry C1 is propagated to 2^{nd} adder, we get the carry output of 2nd adder at t=4Δ and at t=5Δ we get the S2. At t=4Δ we have carry available at

3rd adder so its carry output comes at t=6Δ and sum output comes at t=7Δ. Similarly we get the final carry of 4 bit parallel adder at t=8Δ and sum S4 & hence complete output at t=9Δ.

And for n-bit adder we have the total time taken as 2 * (n-1) Δ + 3Δ = (2n+1) Δ

For 16-bit adder we have the

**Time delay= (2*16+1) Δ = 33Δ**

which is quiet large