# 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.

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.

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