# Serial and Parallel Subtractors

Similar to the adder case we can have serial and parallel subtractors as shown below:

Serial subtractor:

In this circuit, we have Input number coming bit by bit and output comes bit by bit and the final borrow at the end:

Parallel Subtractor:

All inputs are feed simultaneously.

Borrow-propagate subtractor:

Similar to the case of adder we can have the circuit as follow:

Similar to the adder case we have the delay for n-bit subtractor as (2n+1) Δ and so for 16 bit subtractor as 33Δ.

Borrow look ahead subtractor:

Hence to reduce this time delay we employ another method to design the subtractor same as the case of adder.

So we have the following equations:

B2=G1+P1*B1

B3=G2+P2*B2= G2 + P2*(G1+P1*B1)=G2+G1*P2 + P1*P2*B1

B4=G3+P3*B3=G3 + P3*(G2+G1*P2 + P1*P2*B1)= G3+G2*P3 + G1*P2*P3 + B1*P1*P2*P3

B5=G4+P4*B4= G4 + P4*(G3+G2*P3 + G1*P2*P3 + B1*P1*P2*P3)

= G4 + G3*P4 + G2*P3*P4 + G1*P2*P3*P4 + B1*P1*P2*P3*P4

Similar to the adder circuit we have the delay for borrow look ahead subtractor is for a 16-bit adder as

= Δ + 2Δ + 2Δ + 2Δ + 2Δ + 3Δ = 12Δ which is also illustrated below:

And delay is reduced by factor of 3.