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DIGITAL ELECTRONICS 
SUBTRACTORS LOGICAL CIRCUIT
Objectives 
 Subtractors 
 Types of subtractor 
1. Half subtractor 
 Truth table 
 Boolean Expression 
 Logic circuit 
2. Full subtractor 
 Truth table 
 Boolean Expression 
 Logic circuit 
 Parallel binary subtractor
What is Subtractors? 
Subtractor is the one which is 
used to subtract two binary 
numbers and provides Difference 
and Borrow as an output.
Type of Subtractors 
 Half Subtractor 
 Full Subtractor
 Half subtractor 
Half Subtractor is used for subtracting one single bit 
binary number from another single bit binary number. 
It has two inputs, A (minuend) and B (subtrahend) and 
two outputs Difference and Borrow.
Truth Table 
Input Output 
A B Difference Borrow 
0 0 0 0 
0 1 1 1 
1 0 1 0 
1 1 0 0
Boolean Expression 
From the truth table, Boolean Expression can be 
derived as: 
Difference = A’B + AB’ = A ⊕ B 
Borrow = A’B
Logical Circuit
 Full Subtractor 
A logic Circuit Which is used for Subtracting 
three Single bit Binary numbers is known as Full 
Subtractor. It has three inputs, A(minuend) and 
B(subtrahend) and C(subtrahend) and two outputs 
Difference and Borrow.
Truth Table 
Input Output 
A B C D B 
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
Boolean Expression 
From the truth table, Boolean Expression can be 
derived as: 
D = A ⊕ B ⊕ C 
B = BC + (B ⊕ C) A
Logical Circuit
Parallel Binary Subtractor 
Parallel binary subtractor can be implemented by cascading 
several full-subtractors. 
Next slide shows the block level representation of a 4-bit 
parallel binary subtractor, which subtracts 4-bit b3b2b1b0 from 
4-bit a3a2a1a0. It has 4-bit difference output D3D2D1D0 with 
borrow output Bout.
Diagram
Any question ?
THANK YOU

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logical circuits substractors

  • 2. Objectives  Subtractors  Types of subtractor 1. Half subtractor  Truth table  Boolean Expression  Logic circuit 2. Full subtractor  Truth table  Boolean Expression  Logic circuit  Parallel binary subtractor
  • 3. What is Subtractors? Subtractor is the one which is used to subtract two binary numbers and provides Difference and Borrow as an output.
  • 4. Type of Subtractors  Half Subtractor  Full Subtractor
  • 5.  Half subtractor Half Subtractor is used for subtracting one single bit binary number from another single bit binary number. It has two inputs, A (minuend) and B (subtrahend) and two outputs Difference and Borrow.
  • 6. Truth Table Input Output A B Difference Borrow 0 0 0 0 0 1 1 1 1 0 1 0 1 1 0 0
  • 7. Boolean Expression From the truth table, Boolean Expression can be derived as: Difference = A’B + AB’ = A ⊕ B Borrow = A’B
  • 9.  Full Subtractor A logic Circuit Which is used for Subtracting three Single bit Binary numbers is known as Full Subtractor. It has three inputs, A(minuend) and B(subtrahend) and C(subtrahend) and two outputs Difference and Borrow.
  • 10. Truth Table Input Output A B C D B 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
  • 11. Boolean Expression From the truth table, Boolean Expression can be derived as: D = A ⊕ B ⊕ C B = BC + (B ⊕ C) A
  • 13. Parallel Binary Subtractor Parallel binary subtractor can be implemented by cascading several full-subtractors. Next slide shows the block level representation of a 4-bit parallel binary subtractor, which subtracts 4-bit b3b2b1b0 from 4-bit a3a2a1a0. It has 4-bit difference output D3D2D1D0 with borrow output Bout.