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DIGITAL LOGIC DESIGN 1st

The basic and most important DLD slides of 1st lecture

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DIGITAL LOGIC DESIGN 1st

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  1. DIGITAL LOGIC DESIGN Lecture #1 Sawera Kanwal Lecturer Department of Computer Science sawerakanwal@ncbae.edu.pk

  2. Fundamental of DLD What is a binary number system? A number system where a number is represented by using only two digits (0 and 1) with a base 2 is called a binary number system. For example, (1001) is a binary number. What is a bit? A bit is a single digit in the binary number. For example, 101 is a three-bit binary number, where 1, 0 and 1 are the bits. Book: Digital Fundamentals by Floyd, 11/e

  3. NUMBER SYSTEM Number systems are the technique to represent numbers in the computer system architecture, every value that you are saving or getting into/from computer memory has a defined number system. The number system is simply a system to represent or express numbers. There are various types of number systems and the most commonly used ones are decimal number systems, binary number systems, octal number systems, and hexadecimal number systems. Computer architecture supports the following number of systems. 1. Binary number system 2. Octal number system 3. Decimal number system 4. Hexadecimal (hex) number system

  4. Conversion in Binary

  5. BINARY NUMBER SYSTEM • BINARY NUMBER SYSTEM A Binary number system has only two digits that are 0 and 1. Every number (value) represents 0 and 1 in this number system. The base of the binary number system is 2, because it has only two digits.

  6. Example The binary system is applied internally by almost all latest computers and computer-based devices because of its direct implementation in electronic circuits using logic gates. Every digit is referred to as a bit. Example: Convert 4 in binary Solution: 4 in binary is (100)2

  7. Example

  8. Overview

  9. Binary Arithmetic Operations The arithmetic operations in numbers, in the same way, we can perform addition, subtraction, multiplication and division operations on Binary numbers. Let us learn them one by one. Binary Addition Adding two binary numbers will give us a binary number itself. It is the simplest method. The addition of two single-digit binary numbers is given in the table below. Binary Numbers Addition 0 0 0 0 1 1 1 0 1 1 1 0; Carry →1

  10. Let us take an example of two binary numbers and add them. For example: Add 11012 and 10012.Solution: 

  11. Binary Subtraction Subtracting two binary numbers will give us a binary number itself. It is also a straightforward method. The subtraction of two single-digit binary numbers is given in the table below. Binary Numbers Subtraction 0 0 0 0 1 1; Borrow 1 1 0 1 1 1 0

  12. Binary MultiplicationThe multiplication process is the same for binary numbers as it is for numerals. Let us understand it with an example.Example: Multiply 11012 and 10102.Solution: 

  13. Binary Division The binary division is similar to the decimal number division method. We will learn with an example here.

  14. Thank You

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