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To Study of Half-Subtractor using Logic gates and verification with Truth Table.

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Apparatus required:-The following electronics components are required.
  •  EX-OR Gate (IC-7486)
  •  AND Gate (IC-7408)
  •  NOT Gate (IC-7404)
  •  Digital Trainer KIT
  •  Breadboard
  •  Connecting wires
Description:- 
Subtractor is a combinational circuit that performs subtraction of two bits and has two inputs and two outputs. The two inputs denoted by A and B represents minuend and subtrahend. The two outputs are the difference “D” and the borrow bit “Bo“.
 
The half Subtractor is constructed using X-OR & AND Gate. The half Subtractor has two input and two outputs. The outputs are difference and borrow. The difference can be applied using X-OR Gate, borrow output can be implemented using an AND Gate and an inverter. 
 
Suppose the minuend bit is x and the subtrahend bit is y. If we want to perform x-y, we have to check the relative magnitude between x and y. If x>/y, we have three possibilities: 0-0=0, 1-0=1 and 1-1=0. The result is known as difference bit. If x
 
Symbol:-
 
  
 Truth-Table:-
  
 K-Map for DIFFERENCE: DIFFERENCE = A’B + AB’
 
 
K-Map for BORROW: BORROW = A’B
  
 
Boolean Expression: - 
Inputs are A and B Then D = A XOR B and B0= (NOT A).B
 
Procedure to Perform:-
  •  Take Digital Trainer KIT including Breadboard, IC 7408 (AND) and IC 7486 (EX-OR) and connecting leads (wires).
  •  Insert ICs on the Breadboard.
  •  According to pin configuration of ICs perform the connections.
  •  Connect VCC (+5V) to pin no.14 and Connect Pin no. 7 to GND of ICs.
  •  Connect one gate input connections to the input switches D0 and D1 on Digital IC Trainer KIT for IC (XOR Gate); these are connection for adding the input.
  •  Connect same input connections to the input switches D0 and D1 on Digital IC Trainer KIT for IC (AND Gate); these are connection for the Carry.
  •  Switch On the Digital IC Trainer KIT.
  •  Now Verify after Apply the various combination of Truth table and verify the output at LEDs for Half-Adder.
  •  If output LED glows RED it shows logic Low or 0.
  •  Switch off the Digital Trainer KIT after performing the Experiment.
  •  Disconnect Output from the LED and note down the corresponding multi-meter voltage reading for various combinations of inputs (not required).
Conclusion: - All the output verified the result of Truth Table.
 
Precaution in lab:-
  •  All the connections should be tight and proper.
  •  Handle the ICs carefully.
  •  Check the connection once again before Switching on the Digital Trainer KIT.
  •  Switch of the Trainer Kit after performing the Experiment.

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