# Digital Electronics Number System And Binary Codes Pdf

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- Binary-coded decimal
- Digital Number System
- Digital Electronics - Number Systems and Codes
- Module 1.0

## Binary-coded decimal

Filling the register with non-significant zeros is fine - if the number is smaller than the maximum value the register will hold, but how about larger numbers? These must be dealt with by dividing the binary number into groups of 8 bits, each of which can be stored in a one-byte location, and using several locations to hold the different parts of the total value. Just how the number is split up depends on the design of the electronic system involved. Top of Page. Hons All rights reserved. Revision

## Digital Number System

In computing and electronic systems, binary-coded decimal BCD is a class of binary encodings of decimal numbers where each digit is represented by a fixed number of bits , usually four or eight. Sometimes, special bit patterns are used for a sign or other indications e. In byte -oriented systems i. The precise 4-bit encoding, however, may vary for technical reasons e. BCD's main virtue, in comparison to binary positional systems , is its more accurate representation and rounding of decimal quantities, as well as its ease of conversion into conventional human-readable representations. Its principal drawbacks are a slight increase in the complexity of the circuits needed to implement basic arithmetic as well as slightly less dense storage.

The octal numeral system , or oct for short, is the base -8 number system, and uses the digits 0 to 7. Octal numerals can be made from binary numerals by grouping consecutive binary digits into groups of three starting from the right. For example, the binary representation for decimal 74 is Two zeroes can be added at the left: 00 1 , corresponding the octal digits 1 1 2 , yielding the octal representation The Yuki language in California and the Pamean languages [1] in Mexico have octal systems because the speakers count using the spaces between their fingers rather than the fingers themselves.

If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Donate Login Sign up Search for courses, skills, and videos. Math Algebra all content Introduction to algebra Binary and hexadecimal number systems. Introduction to number systems and binary. Hexadecimal number system.

## Digital Electronics - Number Systems and Codes

The reflected binary code RBC , also known just as reflected binary RB or Gray code after Frank Gray , is an ordering of the binary numeral system such that two successive values differ in only one bit binary digit. For example, the representation of the decimal value "1" in binary would normally be "" and "2" would be "". In Gray code, these values are represented as "" and "".

In our previous section, we learned different types of number systems such as binary, decimal, octal, and hexadecimal. In this part of the tutorial, we will learn how we can change a number from one number system to another number system. As, we have four types of number systems so each one can be converted into the remaining three systems. There are the following conversions possible in Number System. There are three conversions possible for binary number, i.

### Module 1.0

Solved examples with detailed answer description, explanation are given and it would be easy to understand. Here you can find objective type Digital Electronics Number Systems and Codes questions and answers for interview and entrance examination. Multiple choice and true or false type questions are also provided. You can easily solve all kind of Digital Electronics questions based on Number Systems and Codes by practicing the objective type exercises given below, also get shortcut methods to solve Digital Electronics Number Systems and Codes problems.

The Web This site. Ask most people what the most commonly used number system is, and they would probably reply after a bit of thought , the decimal system. But actually many number systems, and counting systems are used, without the users thinking much about it. For example clocks and compasses use the ancient Babylonian number system based on 60 rather than the decimal system based on Because 60 is easier to divide into equal segments, it can be evenly divided by 1,2,3,4,5,6,10,12,15, 20 and This is much better for applications such as time, or degrees of angle than a base of 10, which can only be divided into equal parts by 1, 2 and 5. Many counting systems are ancient in origin and are still in use because they are useful for particular purposes.

Electronic and Digital systems may use a variety of different number systems, e. Decimal, Hexadecimal, Octal, Binary. In the above, d n-1 to d 0 is integer part, then follows a radix point, and then d -1 to d -m is fractional part. How to convert a number from one base to another? Follow the example illustrations:. Note: Keep multiplying the fractional part with 2 until decimal part 0.

octal number can be converted into a binary number by converting each of the Many modern digital computers employ the binary (base-2) number system to represent In some cases circuits are included which indicate when an error has.

The binary system is a number system where numbers are represented using the digits 0 and 1. It is used in the computers, since they work with two voltage levels, and thus their natural number system is the binary system 1 - ON, 0 - OFF. The hexadecimal number system or hexadecimal system sometimes shortened as Hex is a number system that uses 16 symbols: from 0 to 9 and A, B, C, D, E and F. Its current use is highly linked to Computer Science, since the computers use the byte or octet as a basic memory unit.

In a digital system, the system can understand only the optional number system. In these systems, digits symbols are used to represent different values, depending on the index from which it settled in the number system. In simple terms, for representing the information, we use the number system in the digital system. In the digital computer, there are various types of number systems used for representing information.

Definition : In digital electronics, the number system is used for representing the information. The number system has different bases and the most common of them are the decimal, binary, octal, and hexadecimal. The base or radix of the number system is the total number of the digit used in the number system. Suppose if the number system representing the digit from 0 — 9 then the base of the system is the The number system is having digit 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; this number system is known as a decimal number system because total ten digits are involved.

*Each Hexadecimal Number digit can represent a 4-bit Binary Number. Sum each product term to get a decimal equivalent number. Take, for example, the number *

The binary number system , also called the base-2 number system , is a method of representing numbers that counts by using combinations of only two numerals: zero 0 and one 1. Computers use the binary number system to manipulate and store all of their data including numbers, words, videos, graphics, and music. The term bit, the smallest unit of digital technology, stands for "BInary digiT. A kilobyte is 1, bytes or 8, bits. Base and base number systems are more compact than the binary system.

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A digital system can understand positional number system only where there are a few symbols called digits and these symbols represent different values depending on the position they occupy in the number.

Chapter 1: Digital Systems and Binary Numbers •Binary values are represented abstractly by: – digits 0 and 1 necessary to have a basic knowledge of digital circuits and their logical •A popular code used to represent information sent.

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