adders
DESCRIPTION
TRANSCRIPT
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Basic Adders+
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What is Adder?
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Adder :
In electronics an adder is digital circuit that perform addition of numbers.
In modern computer adder reside in the arithmetic logic unit (ALU).
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Adders :
Adders are important not only in the computer but also in many types of digital systems in which the numeric data are processed.
Types of adder:
1. Half adder
2. Full adder
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Half adder :
The half adder accepts two binary digits on its inputs and produce two binary digits outputs, a sum bit and a carry bit.
Carrycoutinput
input Sum
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Full adder :
The full adder accepts two inputs bits and an input carry and generates a sum output and an output carry.
input
input
A Sum
Carry
B
Cout Cin
input
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Half adder to Full adder
input
input
A
B
A
B
Sum
Cout
Half adder Half adder
Cin
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Truth Table of Adder
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Truth Table of AdderA B Cin Cout ∑
0 0 0 0 0
0 0 1 0 1
0 1 0 0 1
0 1 1 1 0
1 0 0 0 1
1 0 1 1 0
1 1 0 1 0
1 1 1 1 1
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Truth Table of AdderA B Cin Cout ∑
0 0 0 0 0
0 0 1 0 1
0 1 0 0 1
0 1 1 1 0
1 0 0 0 1
1 0 1 1 0
1 1 0 1 0
1 1 1 1 1
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Truth Table of AdderA B Cin Cout ∑
0 0 0 0 0
0 0 1 0 1
0 1 0 0 1
0 1 1 1 0
1 0 0 0 1
1 0 1 1 0
1 1 0 1 0
1 1 1 1 1
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Truth Table of AdderA B Cin Cout ∑
0 0 0 0 0
0 0 1 0 1
0 1 0 0 1
0 1 1 1 0
1 0 0 0 1
1 0 1 1 0
1 1 0 1 0
1 1 1 1 1
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Truth Table of AdderA B Cin Cout ∑
0 0 0 0 0
0 0 1 0 1
0 1 0 0 1
0 1 1 1 0
1 0 0 0 1
1 0 1 1 0
1 1 0 1 0
1 1 1 1 1
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Truth Table of AdderA B Cin Cout ∑
0 0 0 0 0
0 0 1 0 1
0 1 0 0 1
0 1 1 1 0
1 0 0 0 1
1 0 1 1 0
1 1 0 1 0
1 1 1 1 1
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Truth Table of AdderA B Cin Cout ∑
0 0 0 0 0
0 0 1 0 1
0 1 0 0 1
0 1 1 1 0
1 0 0 0 1
1 0 1 1 0
1 1 0 1 0
1 1 1 1 1
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Truth Table of AdderA B Cin Cout ∑
0 0 0 0 0
0 0 1 0 1
0 1 0 0 1
0 1 1 1 0
1 0 0 0 1
1 0 1 1 0
1 1 0 1 0
1 1 1 1 1
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A
B
Circuit of Adder
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A
BX
Circuit of Adder
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A
B
Cin
∑
Circuit of Adder
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A
B
Cin
∑
Y
Circuit of Adder
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A
B
Cin
∑
= A.B
Y
Circuit of Adder
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A
B
Cin
∑
Cout
Cout= (A B). Cin + A.B
Circuit of Adder
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A
B
Cin
∑
Cout
Verification of Truth TableA B Cin
0 0 0
Cout ∑
0 0
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A
B
Cin
∑
Cout
Verification of Truth TableA B Cin
0 0 1
Cout ∑
0 1
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A
B
Cin
∑
Cout
Verification of Truth TableA B Cin
0 1 0
Cout ∑
0 1
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A
B
Cin
∑
Cout
Verification of Truth TableA B Cin
0 1 1
Cout ∑
1 0
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A
B
Cin
∑
Cout
Verification of Truth TableA B Cin
1 0 0
Cout ∑
0 1
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A
B
Cin
∑
Cout
Verification of Truth TableA B Cin
1 0 1
Cout ∑
1 0
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A
B
Cin
∑
Cout
Verification of Truth TableA B Cin
1 1 0
Cout ∑
1 0
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A
B
Cin
∑
Cout
Verification of Truth TableA B Cin
1 1 1
Cout ∑
1 1
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Applications of Adder
THE BCD ADDER
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BCD Adder
• Binary Coded Decimal Adder
• Just adds decimal digits
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Binary Coded Decimal
• It is possible to represent decimal numbers simply by encoding each decimal digit in binary form called binary coded decimal
• Because there are 10 digits to represent, it is necessary to use four bits per digit.
From 0=0000 to 9=1001 by using 8421 code. For example: Convert 98 into BCD. 9 8 1001 1000 BCD representation was used in some early computers and many
handheld calculators.
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Decimal DigitsDecimal Number BCD Equivalent
0 0000
1 0001
2 0010
3 0011
4 0100
5 0101
6 0110
7 0111
8 1000
9 1001
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The BCD Adder
• BCD is a numerical code and can be used in arithmetic operations.• Addition is the most important operation in BCD.• Following are the steps to perform addition:
Step1Add the two BCD numbers, using the rules for binary
addition.
Step2If a 4-bit sum is equal to or less than 9, it is a valid BCD
number.
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THE BCD ADDER
• Add the following BCD number
0011 + 0100
0011 3
+ 0100 + 4
0111 7
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4-Bit Adder• A single full –adder is capable of adding two 1-bit numbers and
input carry.
• What happens if we want to add binary numbers with more than 1-bit?
• The concept of additional full-adders must be used i.e. to add 2-bit numbers two adders must be needed and to add 4-bit numbers four adders must be needed.
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4-Bit Adder
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Thanks!