Basic Adders : Basic Adders +
Presented By : Presented By Muhammad Yasir
Shahid Mehboob
Syed Faran Sattar
Muhammad Bacha Hussain
Saba Minhas
Ayesha Zahoor
Sairah Batool
What is Adder? : What is Adder? Shahid Mehboob
Roll No. 5733
Slide 4: Adder :
In electronics an adder is digital circuit that perform addition of numbers.
In modern computer adder reside in the arithmetic logic unit (ALU).
Slide 5: 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:
Half adder
Full adder
Slide 6: 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.
Slide 7: Full adder :
The full adder accepts two inputs bits and an input carry and generates a sum output and an output carry.
Half adder to Full adder : Half adder to Full adder
Truth Table of Adder : Truth Table of Adder Syed Faran Sattar
Roll No. 5730
Truth Table of Adder : Truth Table of Adder
Truth Table of Adder : Truth Table of Adder
Truth Table of Adder : Truth Table of Adder
Truth Table of Adder : Truth Table of Adder
Truth Table of Adder : Truth Table of Adder
Truth Table of Adder : Truth Table of Adder
Truth Table of Adder : Truth Table of Adder
Truth Table of Adder : Truth Table of Adder
Truth Table of Adder : Truth Table of Adder
Circuit of Adder : Circuit of Adder Muhammad Bacha Hussain
Roll No. 5726
Circuit of Adder : A B Circuit of Adder
Circuit of Adder : A B X Circuit of Adder
Circuit of Adder : A B Cin ? Circuit of Adder
Circuit of Adder : A B Cin ? Y Circuit of Adder
Circuit of Adder : A B Cin ? = A.B Y Circuit of Adder
Circuit of Adder : A B Cin ? Cout Cout= (A B). Cin + A.B Circuit of Adder
Verification of Truth Table : Verification of Truth Table Ayesha Zahoor
Roll No. 5722
Verification of Truth Table : A B Cin ? Cout Verification of Truth Table
Verification of Truth Table : A B Cin ? Cout Verification of Truth Table
Verification of Truth Table : A B Cin ? Cout Verification of Truth Table
Verification of Truth Table : A B Cin ? Cout Verification of Truth Table
Verification of Truth Table : A B Cin ? Cout Verification of Truth Table
Verification of Truth Table : A B Cin ? Cout Verification of Truth Table
Verification of Truth Table : A B Cin ? Cout Verification of Truth Table
Verification of Truth Table : A B Cin ? Cout Verification of Truth Table
BCD Adder : BCD Adder Saba Minhas
Roll No. 5734
Applications of Adder : Applications of Adder THE BCD ADDER
BCD Adder : BCD Adder Binary Coded Decimal Adder
Just adds decimal digits
Binary Coded Decimal : 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.
Decimal Digits : Decimal Digits
The BCD Adder : 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:
Step1 Add the two BCD numbers, using the rules for binary
addition.
Step2
If a 4-bit sum is equal to or less than 9, it is a valid BCD
number.
THE BCD ADDER : THE BCD ADDER Add the following BCD number
0011 + 0100
0011 3
+ 0100 + 4
0111 7
4-Bit Adder : 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.
4-Bit Adder : 4-Bit Adder
BCD Adder : BCD Adder Muhammad Yasir
Roll No. 5727
Problem with 4-bit Adder : Problem with 4-bit Adder 1 + 1 = 2
1 + 1 = 10
0001 + 0001 = 0010 1 + 5 = 6
1 + 101 = 110
0001 + 0101 = 0110
Problem with 4-bit Adder : Problem with 4-bit Adder 1 + 8 = 9
1 + 1000 = 1001
0001 + 1000 = 1001 1 + 9 = 10
1 + 1001 = 1010
0001 + 0101 = 0001 0000
Problem With 4-bit Adder : Problem With 4-bit Adder Results > 9 are Not Correct
Need Correction
Solution : Solution The Difference is Always 6
Add 6 to the Result
The Corrected BCD Adder : The Corrected BCD Adder Take input bits to the 4-bit adder
Check if result >9
If it is not, then return as it is
If it is, add 6 to it and return
Implementing the Logic : Implementing the Logic Circuit to check if result > 9
Input BCD A: A3A2A1A0
Input BCD B: B3B2B1B0
Result BCD: S3S2S1S0
Implementing the Logic : Implementing the Logic Remember:610 = 0110BCD
Summary : Summary Sairah Batool
Roll No. 5732
Summary : Summary The Adders
Cout = A.B + (A ? B).Cin
? = A ? B ? Cin
Multi-bit Adder (e.g. 4-bit Adder)
Applications and Uses of Adder
Q/A Session : Q/A Session
Thanks! : Thanks!