To verify the truth table of half and full subtractor

Aim

To verify the truth table of half and full subtractor.

Apparatus Required:

Digital trainer kit, IC 7486, IC 7432, IC 7408, IC 7404 Connecting wires.

Theory

Half Subtractor

A half subtractor is a logical circuit that performs a subtraction operation on two single binary digits. The half subtractor produces a difference and a borrow bit for the next stage.

From the truth table of the half subtractor we can see that the difference (D) output is the result of the Exclusive-OR gate and the Borrow-out (B) is the result of the NOT-AND combination. Then the Boolean expression for a half subtractor is as follows.

For the difference bit:

D = X XOR Y = X ⊕ Y

For the Borrow bit

B = not-X AND Y = X.Y

Full Subtractor

A full subtractor has three inputs. The two single bit data inputs X (minuend) and Y(subtrahend) the same as before plus an additional Borrow-in (B-in) input to receive the borrow generated by the subtraction process from a previous stage as shown below.

For the difference(D)bit:

D = (X’.Y’.Bin) + (X’.Y.Bin’) + (X.Y’.Bin’) + (X.Y.Bin)

which can be simplified too:

D = (X XOR Y) XOR Bin = (X ⊕ Y) ⊕ Bin

For the borrow out (Bout) bit:

Bout = (X’.Y’.Bin) + (X’.Y.Bin’) + (X’.Y.Bin) + (X.Y.Bin)

which will also simplify too:

Bout = X’ AND Y OR (X XOR Y)’Bin = X’.Y + (X ⊕ Y)’Bin

Procedure:-

1. Place the breadboard gently on the observationtable
2. Fix the IC which is under observation between the half shadow lineof breadboard, so there is no shortage ofvoltage.
3. Connect the wire to the main voltage source (Vcc) whose other end is connected to last pin of the IC (14 place from thenotch).
4. Connect the ground of IC (7th place from the notch) to the ground terminal provided on the digital labkit.
5. Give the input at the gate of the ICs by using connecting wires. (In accordance toIC provided).
6. Connect output pins to the led on digital labkit.
7. Switch on the powersupply.
8. If led glows then output is true, if it doesn’t glow output is false, which is numerically denoted as 1 and 0respectively.
9. Verify the truthtable.

Precautions:

1. All ICs should be checked before starting theexperiment.
2. All the connection should betight.
3. Always connect ground first and then connectVcc.
4. Suitable type wire should be used for different types ofcircuit.
5. The kit should be off before changing theconnections
6. after the completion of experiment, switch off the supply of theapparatus.

Result:The truth table of half subtractor and full subtractor is verified.

Questions:

Q1:What is a combinationalcircuit?

Ans:In a combinational circuit, the output depends upon present input(s) only i.e, not dependant on the previous input(s). The combinational circuit has no memory element. It consists of logic gates only

Q2:What is ahalf-subtractor?

Ans:A logic circuit, that can subtracts two 1-bit numbers and produce outputs for difference and borrow, is called a half- subtractor.

Q3:What is a full-subtractor?

Ans:A binary subtractor, which can subtracts two 1-bit binary numbers along with a borrow bit and produces outputs for difference and borrow is called a full- subtractor.