Experiment 5 - Study of Adders
Objective: To realize and implement
a)
Full adder using logic gates and bread board
b)
Half Adder and Full adder using Cedar simulator program.
c)
Four bit Adder using IC 4008.
Components Required : IC 7486, IC 7408, IC 7432, IC 4008, Mini Digital Training and Digital
Electronic Sets.
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.
Truth table
A
B
S
C
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
The Boolean functions describing the half-adder according to the truth table are:
S  AB  AB  A  B
C  AB
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 according to the truth table are:
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Truth table
A
B
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
Sum
Carry
0
1
1
0
1
0
0
1
0
0
0
1
0
1
1
1
Sum  ABCin  ABCin  ABCin  ABCin  ( AB  AB)Cin  ( AB  AB)Cin
Sum  ( A  B)Cin  ( A  B)Cin  ( A  B)  Cin
Carry  ABCin  ABCin  ABCin  ABCin  ( AB  AB)Cin  (Cin  Cin) AB  ( A  B)Cin  AB
Binary Adder: It’s a digital circuit that produces the arithmetic sum of two binary numbers. It
can be constructed with full adders connected in cascade with the output carry from each full
adder connected to the input carry of the next full adder in the chain. Figure 3 is showing an
example of four bit binary adder to get the sum of A+B, where, A= A3A2A1A0 and B = B3B2B1B0, S
denote to the sum and C denote to the carry.
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IC 4008 is a binary adder with 16 pin and it can be identified as a function integrate. Binary adder
of 4008 finds the sum of two 4-bit numbers and Cin.
1 1 1 0
1 1 1 0
+1 0 1 0
1 0 1 0
----------------+ 1
------- Cin
1 1 0 0 0
-------------1 1 0 0 1
Procedures:
1- Implement full adder using IC’s and bread board.
2- Repeat the steps in 1 using Cedar simulator.
3- Implement the four bit binary adder using the IC 4008.
Conclusions: Thus half adder, full adder, and binary adder are studied.
More Information:
Half Subtractor: Subtracting a single-bit binary value B from another A (A-B) produces a
difference bit D and a borrow out bit Brr. This operation is called half subtraction and the circuit
to realize it is called a half subtractor.
Truth table
A B D
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
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The Boolean functions describing the half-Subtractor according to the truth table are:
D  AB  AB  A  B
Brr  AB
Full Subtractor: Subtracting two single-bit binary values B, Bin from a single-bit value A
produces a difference bit D and a borrow out Brr bit. This is called full subtraction.
Truth table
A
B Bin
D
Brr
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
1
The Boolean functions describing the full-subtractor according to the truth table are:
D  ABBin  AB Bin  AB Bin  ABBin  ( AB  AB) Bin  ( AB  AB) Bin
D  ( A  B)Bin  ( A  B) Bin  ( A  B)  Bin  ( B  Bin )  A
Brr  ABBin  AB Bin  ABBin  ABBin  A( BBin  B Bin )  BBin ( A  A)  ( B  Bin ) A  BBin
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