“To design & construct Half Adder & Half Subtractor & Perform Binary Operation”
“To design & construct Half Adder & Half
Subtractor & Perform Binary Operation”
1. Objective:
The main objective is to design and verify the truth table of
i.
Half
Adder
ii.
Half
Subtractor
2. Components:
i.
Bread
Board
ii.
Connecting
Wires
iii.
LED
iv.
Battery
v.
3 IC’s
a. IC 7486 for XOR Gate
b. IC 7408 for AND Gate
c. IC 7404 for NOT Gate
3. Introduction:
3.1.Bread Board:
A
bread board is an electronic board into which the electrical components like
diodes and resistors are placed. The sockets of bread board are sturdy and
rugged. Diodes or other electrical components should be placed without making
any damage to the board.
3.2.Integrated Circuits:
A circuit of transistors, resistors, and capacitors constructed on a single semiconductor wafer or chip, in which the components areinterconnected to perform a given function. IC’s consume very little current, generate comparatively
little heat, and are far more shock-proof and reliable than the older
discrete-component circuits.
An integrated circuit consists of a number of circuit components (e.g. transistors, diodes, resistors
etc.) and them inter connections in a single small package to perform a
complete electronic function. These components are formed and connected within
a small chip of semiconductor material. IC’s can be used as advanced logic
gates. Some IC’s description is given below which can be used for logic gates.
3.3.Light Emitting Diodes:
A light-emitting diode (LED) is a semiconductor device that emits visible
light when an electric current passes through it. LED’s
convert electrical energy to light energy. In electronics, polarity indicates whether a circuit component is symmetric or not.
Being diodes, will only allow current to flow in one direction. And when
there’s no current-flow, there’s no light. The positive side of the LED is
called the “anode” and is marked by having a longer
“lead,” or leg. The other, negative side of the LED is called the “cathode.”
3.4.Half Adder
Adder circuit is a combinational digital circuit that
is used for adding two numbers. Half
adder is a combinational arithmetic circuit that adds two numbers and produces
a sum bit (S) and carry bit (C) as the output. If A and B are the input bits,
then sum bit (S) is the X-OR of A and B and the carry bit (C) will be the AND
of A and B. From this it is clear that a half adder circuit can be easily
constructed using one XOR gate and one AND gate. Half adder is the simplest of
all adder circuit, but it has a major disadvantage. The half adder can
add only two input bits (A and B) and has nothing to do with the carry if there
is any in the input. So if the input to a half adder have a carry, then it will
be neglected it and adds only the A and B bits. That means the binary addition
process is not complete and that’s why it is called a half adder.
The symbol and truth table for a half adder is shown
below:
A
|
B
|
Sum
|
Carry
|
0
|
0
|
0
|
0
|
0
|
1
|
1
|
0
|
1
|
0
|
1
|
0
|
1
|
1
|
0
|
1
|
3.5.Half Subtractor:
The half-Subtractor is a combinational circuit which is
used to perform subtraction of two bits. It has two inputs, X (minuend) and Y
(subtrahend) and two outputs D (difference) and B (borrow). The circuit diagram
and truth table for half Subtractor is shown below:
A
|
B
|
Sum
|
Carry
|
0
|
0
|
0
|
0
|
0
|
1
|
1
|
1
|
1
|
0
|
1
|
0
|
1
|
1
|
0
|
0
|
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 (Bout) is the result of the NOT-AND combination.
4. Circuit Diagram:
For Half Adder
For Half Substractor:
5. Experimental Setup:
For Half Adder:
For Half Subtractor
6. Experimentation:
To design Half Adder:
1. First of all, suitable IC’s for XOR and AND
gate are chosen, i.e. IC 7486 & 7408 respectively.
2. Inserted IC’s on the bread board.
3. As there are 14 pins on IC, 7th
pin is grounded and a positive potential is applied to the 14th pin
via a battery of potential less than 5V.
4. First Input of XOR is connected with input of
AND gate.
5. Second input of XOR is connected with the second
input of AND gate.
6. First LED is inserted on bread board with its
positive terminal connected to the output pin (i.e. 2 in our case) of XOR gate
and negative signal is given to the other terminal.
7. Second LED is inserted on bread board with
its positive terminal connected to the output pin (i.e. 2 in our case) of AND gate and negative signal is given to the other
terminal.
8. Initially negative signal is given to both of
the input terminals OF XOR .i.e. 0 is the input at both terminals.
9. Hence in result Sum & carry both are 0.
10. Then 0 (negative signal) is given to one
terminal and 1(positive terminal) to the other. Sum resulted in 1 & Carry
to 0.
11. Then 1 is given to one terminal and 0 to the
other. Sum resulted in 1 & Carry to 0.
12. Then 1 is given to one terminal and 1 to the
other. Both Sum & Carry bits resulted in 1.
13. Truth table is drawn.
To design Half Subtractor:
1. First of all, a suitable IC for XOR, AND
& NOT gate is chosen, i.e. IC 7486, IC 7408 & 7404 respectively.
2. Inserted IC’s on the bread board.
3. As there are 14 pins on IC, 7th
pin is grounded and a positive potential is applied to the 14th pin
via a battery of potential less than 5V.
4. First input of XOR is connected to the input
of NOT & its output is given to AND gate.
5. Second input of XOR is connected to the
second input of AND gate.
6. LED is inserted on bread board with its
positive terminal connected to the output pin (i.e. 2 in our case) of XOR gate
and negative signal is given to the other terminal.
7. LED is inserted on bread board with its positive
terminal connected to the output pin (i.e. 2 in our case) of AND gate and
negative signal is given to the other terminal.
8. Initially negative signal is given to both of
the input terminals i.e. 0 is the input at both terminals. Difference &
Borrow both are 0.
9. Then 0 is given to the first input of XOR
& 1 to its second input. Both Difference & Borrow bits are 1.
10. Then 1 is given to the first input of XOR
& 0 to its second input. Difference is resulted in 1 & Borrow to 0.
11. Finally, 1 is given to both the inputs, both
bits resulted in 0.
12. Truth Table is drawn.
7. Observations & Calculations:
The truth table for Half Adder which we have observed is shown below:
A
|
B
|
Sum
|
Carry
|
0
|
0
|
0
|
0
|
0
|
1
|
1
|
0
|
1
|
0
|
1
|
0
|
1
|
1
|
0
|
1
|
The truth table for Half Subtractor which we have observed is shown
below:
A
|
B
|
Sum
|
Carry
|
0
|
0
|
0
|
0
|
0
|
1
|
1
|
1
|
1
|
0
|
1
|
0
|
1
|
1
|
0
|
0
|
8. Results & Discussion:
We have designed Half Adders and Half Subtractor circuit by combining
XOR and AND in first case and XOR, NOT & AND gate in second one. As we have
also verified the truth tables of half adders and half Subtractors, we can
deduce some main points from this. The total OR & AND logic gates in IC’s
7432 & 7408 respectively are 4, and 6 NOT logic gates in IC 7404. The
circuit for which LED connected to XOR output is on for different input is
known to be Half Adder. The circuit for which Both LED’s are on once is half
subtractor.
9. Conclusion:
Through this experiment we have designed Half Adders & Subtractor
and their truth tables are verified by using IC’s inserted on bread board along
with LED to show OFF or ON status of output.
10. References:
I.
http://logic.ly/lessons/nor-gate/
IV.
http://www.circuitstoday.com/half-adder
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