This document discusses the implementation of half subtractors and full subtractors using basic logic gates and universal gates. It begins by defining a half subtractor and full subtractor, providing their truth tables. It then shows how to design half and full subtractors using NAND, NOR, and other gates. Circuit diagrams are provided for subtractors built with basic gates as well as those using only NAND or only NOR gates. The purpose is for students to realize subtractor circuits using different gate implementations and understand their logic and components.

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HANDOUT#3b
AIM:
Implementation of half subtractor and full subtractor using basic gate and universal
gates.
LEARNING OBJECTIVES:
- Realize the subtractor circuits using basic gates and universal gates
COMPONENT REQUIRED:
- Logic gates (IC) trainer kit.
- Connecting patch chords.
- IC 7400, IC 7408, IC 7432, IC 7402, IC 7404, IC 7486
Sr. No. Component Specification
1 NOT gate IC7404
2 AND gate IC7408
3 OR gate IC7432
4 NAND gate IC 7400
5 NOR gate IC7402
6 EX-OR gate IC7486
THEORY:
Half Subtractor: A logic circuit for the subtraction of B (subtrahend) from
A(minuend) where A and B are 1-bit numbers is referred to as a half subtractor. In
the following truth table, A and B are two inputs and D (difference) and C(borrow)
Truth table
A B S(sum) C(carry)
0 0 0 0
0 1 1 1
1 0 1 0
1 1 0 0
S(sum) = A B
C(borrow) =

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Half Subtractor using basic gates:
Half subtractor using NAND gate only

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Using only NOR gate
Full Subtractor: Just like Full Adder, we require full subtractor circuit for
performing multibit subtraction wherein a borrow from the previous bit position
may also there.
A full subtractor will have three inputs An (minuend), Bn(subtrahend) and Cn-1
(borrow from previous stage) and two outputs Dn (difference) & Cn(borrow)
Truth table
An Bn Cn-1 Sn(sum) Cn(carry)
0 0 0 0 0
0 0 1 1 0
0 1 0 1 0
0 1 1 0 1
1 0 0 1 0
1 0 1 0 1
1 1 0 0 1
1 1 1 1 1

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Logic Equation:

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Logic Circuit using Basic gates:
For Dn(difference)

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For Cn(borrow)
For Sn and Cn using two half subtractor

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Using NAND gate only
For Dn(difference)

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For Cn(borrow)

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Using only NOR gates:
For Dn(difference)

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For Cn(borrow)
PROCEDURE:
1. Check the components for their working.
2. Insert the appropriate IC into the IC base.
3. Make connections as shown in the circuit diagram.
4. Provide the input data via the input switches and observe the output on
output LEDs
5. Give various combinations of inputs and note down the output with help of
LED for all gate ICs one by one.
RESULT:
Thus we have implemented half subtractor and full subtractor using basic gate and
universal gates