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Laboratory Experiment No: 2 Laboratory Experiment No: 2

Half/Full Adder And

Half/Full Adder And

Half/Full Subtractor

Half/Full Subtractor

Objective:

Objective:

 To realize half/full adder and half/full subtractor.To realize half/full adder and half/full subtractor. 

 Using X-OR and basic gatesUsing X-OR and basic gates

Instruments and Components:

Instruments and Components:

ICs ICs   74867486   74327432   74087408   74047404 Breadboard with power supply (5V, 350 mA)

Breadboard with power supply (5V, 350 mA) Digital Multimeter 

Digital Multimeter  Long nose pliers Long nose pliers

Procedure:

Procedure:

1.

1. Verify Verify the the gates.gates. 2.

2. Make Make the the connections as connections as per per the the circuit diagram.circuit diagram. 3.

3. Switch on Switch on VCC and VCC and apply various combinations of apply various combinations of input according to input according to the truth the truth table.table. 4.

4. Note down Note down the output the output readings for readings for half/full adder and half/full adder and half/full subtractor sum/differencehalf/full subtractor sum/difference and the carry/borrow bit for different combinations of input.

(2)

Circuit Diagram:

Circuit Diagram:

Half Adder using Basic Gates:

Half Adder using Basic Gates:

Full Adder using Basic Gates:

Full Adder using Basic Gates:

Half-Adder

Half-Adder

 A

 A B

B S

S C

C S(V)

S(V) C(V)

C(V)

0 0 0 0 0.11 0.15

0 0 0 0 0.11 0.15

0 1 1 0 2.27 0.15

0 1 1 0 2.27 0.15

1 0 1 0 2.29 0.15

1 0 1 0 2.29 0.15

1 1 0 1 0.13 2.25

1 1 0 1 0.13 2.25

Full-Adder

Full-Adder

 A

 A B

B Cn-1

Cn-1 S

S C

C S(V)

S(V)

C(V)

C(V)

0

0 0

0

0

0

0

0 0

0 0.12

0.12

0.14

0.14

0

0 0

0

1

1

1

1 0

0 2.28

2.28

0.14

0.14

0

0 1

1

0

0

1

1 0

0 2.32

2.32

0.14

0.14

0

0 1

1

1

1

0

0 1

1 0.15

0.15

2.27

2.27

1

1 0

0

0

0

1

1 0

0 2.30

2.30

0.14

0.14

1

1 0

0

1

1

0

0 1

1 0.15

0.15

2.28

2.28

1

1 1

1

0

0

0

0 1

1 0.12

0.12

2.24

2.24

(3)

(a)

(a) Half

Half Subtractor:

Subtractor:

(b)

(b) Full

Full Subtractor:

Subtractor:

Half-Subtractor

Half-Subtractor

 A

 A B

B D

D B

B D(V)

D(V) B(V)

B(V)

0 0 0 0 0.11 0.15

0 0 0 0 0.11 0.15

0 1 1 1 2.29 2.24

0 1 1 1 2.29 2.24

1 0 1 0 2.29 0.15

1 0 1 0 2.29 0.15

1 1 0 0 0.13 0.15

1 1 0 0 0.13 0.15

Full-Subtractor

Full-Subtractor

 A

 A B

B Cn-1

Cn-1 D

D B

B D(V)

D(V) B(V)

B(V)

0

0 0

0

0

0

0

0 0

0 0.12

0.12 0.14

0.14

0

0 0

0

1

1

1

1 1

1 2.30

2.30 2.24

2.24

0

0 1

1

0

0

1

1 1

1 2.29

2.29 2.22

2.22

0

0 1

1

1

1

0

0 1

1 0.15

0.15 2.24

2.24

1

1 0

0

0

0

1

1 0

0 2.29

2.29 0.14

0.14

1

1 0

0

1

1

0

0 0

0 0.15

0.15 0.14

0.14

1

1 1

1

0

0

0

0 0

0 0.11

0.11 0.14

0.14

1

1 1

1

1

1

1

1 1

1 2.30

2.30 2.24

2.24

(4)

Breadboard Layout:

Breadboard Layout:

Half Adder 

Half Adder 

Full Adder 

Full Adder 

(5)

Half Subtractor 

Half Subtractor 

Full Subtractor 

Full Subtractor 

(6)

Conclusion:

Conclusion:

Digital computers perform variety of information tasks. Among the functions Digital computers perform variety of information tasks. Among the functions

encountered are the various arithmetic operations. The most basic arithmetic operation is the encountered are the various arithmetic operations. The most basic arithmetic operation is the addition or subtraction of two binary digits. A binary adder-subtractor is a combinational circuit addition or subtraction of two binary digits. A binary adder-subtractor is a combinational circuit that performs the arithmetic operations of addition and subtraction with binary numbers.

that performs the arithmetic operations of addition and subtraction with binary numbers.

 A half-add

 A half-adder is compoer is composed of osed of one X-OR gane X-OR gate and te and one AND one AND gate that pgate that produces twroduces two binaryo binary outputs from two binary inputs. It adds two one-bit binary numbers (A, B).

outputs from two binary inputs. It adds two one-bit binary numbers (A, B). The output is the The output is the sumsum of the two bits (S) and the carry (C). The C output is 1 only when both inputs are 1. The S output of the two bits (S) and the carry (C). The C output is 1 only when both inputs are 1. The S output represents the least significant bit of the sum.

represents the least significant bit of the sum.

 A full-adde

 A full-adder is a combir is a combinational national circuit that circuit that forms the forms the arithmetic suarithmetic sum of three m of three bits. Itbits. It consists of three inputs (A, B, Cn-1) and two outputs (S, C). The third input, Cn-1, represents consists of three inputs (A, B, Cn-1) and two outputs (S, C). The third input, Cn-1, represents the carry from the previous lower significant position. Two outputs are necessary because the the carry from the previous lower significant position. Two outputs are necessary because the arithmetic sum of three binary digits ranges in value from 0 to 3, and binary 2 or 3 needs two arithmetic sum of three binary digits ranges in value from 0 to 3, and binary 2 or 3 needs two digits. The two outputs are designated by the symbols S for sum and C for carry. The binary digits. The two outputs are designated by the symbols S for sum and C for carry. The binary variable S gives the value of the least significant bit of the sum. The binary variable C gives the variable S gives the value of the least significant bit of the sum. The binary variable C gives the output carry. The full-adder is simply two half-adders joined by an OR gate. The C output is 1 output carry. The full-adder is simply two half-adders joined by an OR gate. The C output is 1 only when two or more inputs are 1.

only when two or more inputs are 1.

 A half-sub

 A half-subtractor is a tractor is a combinaticombinational circuit onal circuit which is usewhich is used to ped to perform subtrarform subtraction of twoction of two bits. It has two inputs, A (minuend) and B (subtrahend) and two outputs D (difference) and B bits. It has two inputs, A (minuend) and B (subtrahend) and two outputs D (difference) and B (borrow). It is made of X-OR gate, NOT gate (Inverter), and AND gate. The B output is 1 only (borrow). It is made of X-OR gate, NOT gate (Inverter), and AND gate. The B output is 1 only when the subtrahend (B) is greater than the minuend (A).

when the subtrahend (B) is greater than the minuend (A).

 As in the

 As in the case of thcase of the adde addition using ition using logic gateslogic gates, a full sub, a full subtractoris madtractoris made by combe by combiningining two half-subtractors and an additional OR-gate. A full subtractor has the borrow in capability and two half-subtractors and an additional OR-gate. A full subtractor has the borrow in capability and so allows cascading which results in the possibility of multi-bit subtraction.

References

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