Hello friends , welcome to ELECTRICAL ENCYCLOPEDIA. In this article we will study about the Parallel Subtractor.
In most of the logic circuit, subtraction between more than 1 bit is carried out which can be accomplished by using several full subtractor. "Number of full subtractors required is equal to the number of bits to be subtracted". For eg- for subtracting two 4-bit number we will require 4 full subtractors which will generate a 4-bit difference output and a borrow output.
The working of parallel subtractor is similar to the parallel adder (click here to read).
All the bits of the minuend (number X₃X₂X₁X₀) and subtrahend (number Y₃Y₂Y₁Y₀) are fed into the subtractor circuit simultaneously.
As shown in the figure below is a 4 bit parallel subtractor.
1. The least significant bit (LSB) i.e, X₀ , Y₀ and B₀ (which is initially 0) are added and results in D₀ and B₁. This borrow B₁ becomes the borrow input to the second stage.
2. Similarly, in the second stage X₁,Y₁ and B₁ are added resulting in D₁ and B₂.This carry B₂ becomes the borrow input to the third stage.
3. In the third stage X₂,Y₂ and B₂ are added resulting in D₂ and B₃. This borrow B₃ becomes the borrow input to the fourth stage.
4. In the fourth stage, X₃,Y₃ and B₃ are added resulting in D₃ and B₄ which is the final output carry. Thus, the circuit results in a difference ( D₃D₂D₁D₀) and a borrow output (B₄).
Note that since the parallel subtractor have simple circuit but its speed of operation is limited because for the operation of each full subtractor, it requires the borrow input from the previous state, this creates a propagation delay through all stages (full subtractor).
In most of the logic circuit, subtraction between more than 1 bit is carried out which can be accomplished by using several full subtractor. "Number of full subtractors required is equal to the number of bits to be subtracted". For eg- for subtracting two 4-bit number we will require 4 full subtractors which will generate a 4-bit difference output and a borrow output.
The working of parallel subtractor is similar to the parallel adder (click here to read).
All the bits of the minuend (number X₃X₂X₁X₀) and subtrahend (number Y₃Y₂Y₁Y₀) are fed into the subtractor circuit simultaneously.
As shown in the figure below is a 4 bit parallel subtractor.
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| 4-BIT FULL SUBTRACTOR |
WORKING OF PARALLEL SUBTRACTOR.
It consists of 4 full subtractor and input to the each full subtractor is Xi , Yi and Bi, and the output will be Di and Bi₊₁. The borrow output of the lower order stage is connected to the borrow input of the next higher order stage.1. The least significant bit (LSB) i.e, X₀ , Y₀ and B₀ (which is initially 0) are added and results in D₀ and B₁. This borrow B₁ becomes the borrow input to the second stage.
2. Similarly, in the second stage X₁,Y₁ and B₁ are added resulting in D₁ and B₂.This carry B₂ becomes the borrow input to the third stage.
3. In the third stage X₂,Y₂ and B₂ are added resulting in D₂ and B₃. This borrow B₃ becomes the borrow input to the fourth stage.
4. In the fourth stage, X₃,Y₃ and B₃ are added resulting in D₃ and B₄ which is the final output carry. Thus, the circuit results in a difference ( D₃D₂D₁D₀) and a borrow output (B₄).
Note that since the parallel subtractor have simple circuit but its speed of operation is limited because for the operation of each full subtractor, it requires the borrow input from the previous state, this creates a propagation delay through all stages (full subtractor).