This document discusses subtractors in digital electronics. It defines a half subtractor and full subtractor, providing their truth tables, boolean expressions, and logic circuits. A half subtractor subtracts one single bit binary number from another and outputs the difference and borrow. A full subtractor subtracts three single bit binary numbers and outputs the difference and borrow. The document also describes how a parallel binary subtractor can be implemented by connecting multiple full subtractors to subtract binary numbers with multiple bits.

1. DIGITAL ELECTRONICS
SUBTRACTORS LOGICAL CIRCUIT

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

8. Logical Circuit

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

12. Logical Circuit

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.

14. Diagram

15. Any question ?

16. THANK YOU