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Implementation of Full-Subtractor using Logic gates and verification with Truth Table.

Written by @
Apparatus required:-The following electronics components are required.
  • EX-OR Gate (IC-7486)
  • AND Gate (IC-7408)
  • OR Gate (IC-7432)
  • NOT Gate (IC-7404)
  • Digital Trainer KIT
  • Breadboard
  • Connecting wires
Description:-
The subtraction of two binary numbers may be accomplished by taking the complement of the subtrahend and adding it to the minuend. By this method, the subtraction operation becomes an addition operation requiring full adders for its machine implementation. It is possible to implement subtraction with logic circuits in a direct manner. By this method, each subtrahend bit of the number is subtracted from its corresponding significant minuend bit to form a different bit. If the minuend bit is smaller than the subtrahend bit, a 1 is borrowed from the next significant position. The fact that a 1 has been borrowed must be conveyed to the next higher pair of bits by means of a binary signal coming out (output) of a given stage and going into (input) the next higher stage. It is same for the half-adder and full-adder, half-subtractor and full-subtractor circuits.
 
The full subtractor is a combination of X-OR, AND, OR, NOT Gates. In a full subtractor the logic circuit should have three inputs and two outputs. The two half subtractor put together gives a full subtractor.
 
Symbol:-
 
  
K-Map for DIFFERENCE: Difference= A’B’C + A’BC’ + AB’C’ + ABC
 
 
K-Map for BORROW: BORROW = A’B + BC + A’C
  
 
 
 Truth-Table:-
 
 
Procedure to Perform:-
  • Take Digital Trainer KIT including Breadboard, IC 7408 EX-OR Gate (IC-7486) AND Gate (IC-7408), OR Gate (IC-7432), NOT Gate (IC-7404), 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 IC.
  •  Connect the inputs to the input switches provided in IC Trainer KIT.
  •  Connect to the Output to the Switches of OP-LEDs.
  •  Apply the various combination of Truth table and verify the output at LEDs.
  •  Disconnect Output from the LED and note down the corresponding multi-meter voltage reading for various combinations of inputs.
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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