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## Presentation Description

This is my first ever presentation given at NUML (National University of Modern Language) on Basic Adders along with my whole group. The subject is Digital Logic and Design... May be worth for someone!

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## Presentation Transcript

### Presented By :

Presented By Muhammad Yasir Shahid Mehboob Syed Faran Sattar Muhammad Bacha Hussain Saba Minhas Ayesha Zahoor Sairah Batool

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.

### Truth Table of Adder :

Truth Table of Adder Syed Faran Sattar Roll No. 5730

### Truth Table of Adder :

A B X Circuit of Adder

A B Cin ? Circuit of Adder

A B Cin ? Y Circuit of Adder

A B Cin ? = A.B Y 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 Saba Minhas Roll No. 5734

### 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 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 Add the following BCD number 0011 + 0100 0011 3 + 0100 + 4 0111 7

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.

### 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

### Thanks! :

Thanks! 