Computer operations and architecture

1. 4 Bit Binary Decrementer
What is 4 Bit Binary Decrementer ?
It subtracts 1 binary value from the existing binary value stored in the register or in other
words we can simply say that it decreases the existing value stored in the register by 1.
For any n- bit binary decrementer, ‘n’ refers to the storage capacity of the register which
needs to be decremented by 1. So we require ‘n’ number of full adders. Thus, in case of 4 bit
binary decrementer we require 4 full adders.
Working:
It consists of 4 full adders, connected one after the other. Each full adder has 3 inputs (carry
input, 1, A) and 2 outputs (carry output and S)
A full adder basic consist of 2 half adders and an OR gate.
The carry(C) from previous full adder is propagated to the next full adder. So carry output
from one full adder becomes one of the three input of the next full adder.
It follows the concept of 2’s complement, so we take 1 as input in all 4 full adder as seen
from the above diagram.
So we add 1111 in order to subtract 1.

2. Reason for adding 1111:
This is because our main motive is to subtract 1 which in 4 bit representation is 0001
Representing it in 1’s complement will give: 1110
Representing it in 2’s complement (adding 1 to 1’s complement) will give: 1111
This is the reason why input 1111 is given to get a decremented output in 4 bit binary
decrementer.