Binary Subtractor
A Binary Subtractor is a digital circuit that performs the arithmetic binary subtraction between two numbers with respect to the logic operations and legal guidelines of Boolean Algebra.
The subtractors are utilized in combinational circuit design and the Arithmetic Logic Unit (ALU) of the processor to calculate a number of addresses. Subtractor circuits cut back sound distortion in amplifiers and the facility of radio indicators.
There are two sorts of Subtractor circuits-
- Half Subtractors
- Full Subtractors
Half Subtractors
Half Subtractors are a sort of digital circuit that calculates the arithmetic binary subtraction between two single-bit numbers. It’s a circuit with two inputs and two outputs.
For 2 single-bit binary numbers A and B, a half subtractor produces two outputs.
- A is named the Minuend Bit
- B is known as Subtrahend Bit.
- Output D is the distinction between the 2 enter bits (A-B).
- Output P is the earlier borrow between the 2 enter bits (A-B).
The earlier borrow is for essentially the most important bit (MSB).
Operation and Fact Desk for Half Subtractor
Operation:
Case 1: A = 0, B = 0;
In keeping with Binary subtraction, the distinction of those numbers is 0 with no earlier borrow.
0
– 0
一一一一一
0
一一一一一
Therefore, D= 0, P= 0
Case 2: A= 0, B= 1;
In keeping with Binary subtraction, the distinction between these two numbers is 1 with a earlier borrow of 1.
0
– 1
→1 (Earlier Borrow)
一一一一一
1
一一一一一
Therefore, D= 1, P= 1
Case 3: A= 1, B= 0;
As per Binary subtraction, the distinction between these two numbers is 1 with no earlier borrow.
1
– 0
一一一一一
1
一一一一一
Therefore, D= 1, P= 0
Case 4: A= 1, B= 1;
In keeping with Binary subtraction, the distinction between these two numbers is 1 with no earlier borrow.
1
– 1
一一一一一
0
一一一一一
Therefore, D= 0, P= 0
Fact Desk:
| A | B | Distinction (S) | Earlier Borrow (P) |
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
Designing Okay-Map for Half Subtractor
By the Fact Desk, We will design a Karnaugh Map or Okay-Map for Half Subtractor to acquire a Boolean Expression.
We will design a Karnaugh Map or Okay-Map for Half Subtractor to acquire a Boolean Expression.
Karnaugh Map for Distinction of Half Subtractor
By fixing this,
D= A’B + AB’
Karnaugh Map for Earlier Borrow of Half Subtractor
By wanting on the Okay-map, We will conclude, we can conclude;
P= A’•B
This Boolean expression helps us to design a half subtractor with an XOR Gate and AND gate.
The operation of the Half Subtractor is proscribed as a result of it might probably solely subtract two-bit binary digits. It doesn’t account for the borrow of the decrease important stage.
This incapability of the circuit places a limitation on its use. Half Subtractors had been utilized in early microprocessors and primary digital circuits.
Designing Half Subtractor utilizing Fundamental Logic Gates adopted by NAND Gate
As,
D= A’B + AB’
Taking double complement
In keeping with d-Morgan’s legislation,
Equally, for the earlier borrow circuit,
P= A’•B
Taking double complement
Full Subtractor
A full Subtractor is a digital circuit that performs the subtraction of three single-digit binary numbers. This can be a three-input and two-output digital circuit.
For 3 single-bit binary numbers A, B, and P, the complete subtractor circuit generates two single-bit binary outputs D (Distinction), and Q (Borrow Output).
- A is the Minuend.
- B is the Subtrahend.
- P is the Earlier Borrow Bit.
- D is the Distinction between A, B, and P.
- Q is the Borrow Output.
A full Subtractor was made to beat the restrictions of a Half Subtractor.
Full Subtractors are used in-
- Performing Arithmetical capabilities like subtraction in ALU of Microprocessors.
- Digital Calculators
- Digital Units
- Computing Deal with Tables in ALU.
- DSP and networking-based methods.
Operation and Fact Desk for Full Subtractor
Operation:
Case 1: A= 0, B= 0, and P= 0;
The distinction of the three binary numbers 0, 0, and 0 produces a distinction of 0 and generates no borrow output.
0
-0
-0
一一一一一
0
一一一一一
Therefore, D= 0, Q= 0
Case 2: A= 0, B= 0, and P= 1;
The distinction of the three binary numbers 0, 0, and 1 produces a distinction of 1 and generates a borrow output bit.
0
-0
-1
→1
一一一一一
1
一一一一一
Therefore, D= 1, Q= 1
Case 3: A= 0, B= 1, and P= 0;
The distinction of the three binary numbers 0, 1, and 0 produces a distinction of 1 and generates a borrow output bit.
0
-1
→1
-0
一一一一一
1
一一一一一
Therefore, D= 1, Q= 0
Case 4: A= 0, B= 1, and P= 1;
The distinction of the three binary numbers 0, 1, and 1 produces a distinction of 0 and generates a borrow output bit.
0
-1
→1
-1
一一一一一
0
一一一一一
Therefore, D= 0, Q= 1
Case 5: A= 1, B= 0, and P= 0;
The distinction of the three binary numbers 1, 0, and 0 produces a distinction of 1 and generates no borrow output.
1
-0
-0
一一一一一
0
一一一一一
Therefore, D= 1, Q= 0
Case 6: A= 1, B= 0, and P= 1;
The distinction of the three binary numbers 1, 0, and 1 produces a distinction of 0 and generates no borrow output.
1
-0
-1
一一一一一
0
一一一一一
Therefore, D= 0, Q= 0
Case 7: A= 1, B= 1, and P= 0;
The distinction between the three binary numbers 1, 1, and 0 produces a distinction of 0 and generates no borrow output.
1
-0
-0
一一一一一
0
一一一一一
Therefore, D= 0, Q= 0
Case 8: A= 1, B= 1, and P= 1;
The distinction between the three binary numbers 1, 1, and 1 produces a distinction of 1 and generates a borrow output bit.
The distinction between A=1 and B=1 is 0. P=1 will get subtracted from this 0 to provide an output of 1 by producing a borrowed output bit.
1
-1
-1
→1
一一一一一
1
一一一一一
Therefore, D= 1, Q= 1
Fact Desk:
| A | B | P | Distinction (D)
D= A-B-P |
Borrow Output (Q) |
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 1 |
| 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 | 1 |
Designing Okay-Map for Full Subtractor
By the Fact Desk, We will design a Karnaugh Map or Okay-Map for Full Subtractor to acquire a Boolean Expression.
Karnaugh Map for Distinction of Full Subtractor:
By Fixing this,
The phrases 
kind a complement of one another, and the entire equation turns into an EX-OR operation;
Simplifying additional,
Karnaugh Map for Borrow Output of Full Subtractor:
The equation turns into,
That is the tip of the article…..
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