To realize Adder and Substractor

To realize Adder and Substractor

  1:02 AM    Dnyaneshwar Kudande

---

 ADDERS AND SUBSTRACTORS

AIM: To realize

i)  Half Adder and Full Adder

ii)  Half Subtractor and Full Subtractor by using Basic gates and NAND gates

LEARNING OBJECTIVE:

▪     To realize the adder and subtractor circuits using basic gates and universal gates

▪     To realize full adder using two half adders

▪     To realize a full subtractor using two half subtractors

COMPONENTS REQUIRED:

IC 7400, IC 7408, IC 7486, IC 7432, Patch Cords & IC Trainer Kit.

THEORY:

Half-Adder: A combinational logic circuit that performs the addition of two data bits, A and B, is called a half-adder. Addition will result in two output bits; one of which is the sum bit,  S, and the other is the carry bit, C. The Boolean functions describing the half-adder are:

S =A Å B                                        C = A B

Full-Adder: The half-adder does not take the carry bit from its previous stage into account. This carry bit from its previous stage is called carry-in bit. A combinational logic circuit that adds two data bits, A and B, and a carry-in bit, Cin , is called a full-adder. The Boolean functions describing the full-adder are:

S = (x  Å  y) Å Cin                          C = xy + Cin (x Å y)

Half Subtractor: Subtracting a single-bit binary value B from another A (i.e. A -B ) produces  a difference bit D and a borrow out bit B-out. This operation is called half subtraction and the circuit to realize it is called a half subtractor. The Boolean functions describing the half- Subtractor are:

S =A Å B                                        C = A*B

Full Subtractor: Subtracting two single-bit binary values, B, Cin from a single-bit value A produces a difference bit D and a borrow out Br bit. This is called full subtraction. The Boolean functions describing the full-subtracter are:

D = (x  Å  y) Å Cin                         Br= A*B + A(Cin) + B(Cin)

I.                       TO REALIZE HALF ADDER

TRUTH TABLE:                                  BOOLEAN EXPRESSIONS: S=A Å B

                              C=A.B

INPUTS		OUTPUTS
A	B	S	C
0	0	0	0
0	1	1	0
1	0	1	0
1	1	0	1

 i)  Basic Gates  

                                            

ii) NAND Gates

II.                       FULL ADDER

TRUTH TABLE

INPUTS OUTPUTS A B Cin S C 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1

                                 

BOOLEAN EXPRESSIONS: S= A Å B Å C

                                                    C=A B + B Cin + A Cin

i) BASIC GATES

ii)  NAND GATES

 

III.                       HALF SUBSTRACTOR

TRUTH TABLE                                             

    

INPUTS OUTPUTS A B D Br 0 0 0 0 0 1 1 1 1 0 1 0 1 1 0 0  BOOLEAN EXPRESSIONS: D=A Å B   Br = AB

  i) BASIC Gate                                                                                                                

ii) Using NAND Gate:

Full Substractor Truth Table:

INPUTS OUTPUTS A B Cin D Br 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 0 1 0 1 0 0 1 1 0 0 0 1 1 1 1 1

BOOLEAN EXPRESSIONS: D= A Å B Å C

Br= A B + B Cin + A Cin

i)   BASIC GATES

PROCEDURE:

·        Check the components for their working.

·        Insert the appropriate IC into the IC base.

·        Make connections as shown in the circuit diagram.

·        Verify the Truth Table and observe the outputs.

RESULT: The truth table of the above circuits is verified. VIVA QUESTIONS:

1)  What is a half adder?

2)  What is a full adder?

3)  What are the applications of adders?

4)  What is a half subtractor?

5)  What is a full subtractor?

6)  What are the applications of subtractors?

7)  Obtain the minimal expression for above circuits.

8)  Realize a full adder using two half adders

9)  Realize a full subtractors using two half subtractors