# Chapter 1 _ Number System a.

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Chapter 1 : Number System and Binary Code (Part 1) | Digital Electronics http://ptuece.loremate.com/die/node/1 Digital Electronics Press Ctrl & '+' To enlarge text and pics! Chapters Home Topics Chapter 1 : Number System and Binary Code (Part 1) Chapter 1 : Part 2 Chapter 2 : Minimization of Logic Function (Part 1) Chapter 2 : Part 2 Chapter 3 : Combinational Logic Circuits (Part 1) Chapter 3 : Part 2 Chapter 4 : Sequential Circuits (Part 1) Chapter 4 : Part 2 Chapter 5 : D/A and A/D Converte
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Digital Electronics Press Ctrl & '+' To enlarge text and pics! Chapters HomeTopicsChapter 1 : Number System andBinary Code (Part 1)Chapter 1 : Part 2Chapter 2 : Minimization of Logic Function (Part 1)Chapter 2 : Part 2Chapter 3 : Combinational LogicCircuits (Part 1)Chapter 3 : Part 2Chapter 4 : Sequential Circuits(Part 1)Chapter 4 : Part 2Chapter 5 : D/A and A/DConverters (Part 1)Chapter 5 : Part 2Chapter 6 : SemiconductorMemoriesChapter 7 : Logic Families Home Chapter 1 : Number System and Binary Code (Part 1)   Remember These:  There are two input signals : analog signals have infinitenumber of distinct values and are continuous, while digitalsignals have finite number of distinct values and arediscrete in nature.Types bf number systems are : decimal, binary, octal,hexadecimal.Codes are representation if digital in specified format whichinclude symbols, alphabets etc.There are two logic levels in digital system : high (1) andlow (0).There are two logic systems positive and negative.Number system is a set of rules and symbols to representnumbers. It can be weighted or non-weighted.Number of values that a character or digit can assume iscalled Radix or Base.Decimal system has radix ‘10’. Leftmost digit is MSD andrightmost digit is LSD.Binary system has radix ‘2’ and two binary digits one ‘1’ and ‘0’. Its weight is expressed as a power of 2.The smallest unit of information is called bit (0 and 1).Binary representation of four bits is called a Nibble.A byte is a combination of 8-binary bits.A word is a combination of 16-binary bits.Octal numbers system has radix ‘8’ and the digits are (0 to7). Its weight is expressed in power of 8.Hexadecimal has radix ‘16’. The digits are 0 to 9 incontinuation with letters A to F Its weight is expressed inpower of 16.l’s complement of a binary number is written by simplyreplacing all 0’s by 1 and all 1’s by 0. Chapter 1 : Number System and Binary Code (Part 1) | Digital Electronicshttp://ptuece.loremate.com/die/node/11 of 121/11/2012 10:14 PM  2’s complement is one increment of l’s complement.Numbers without +ve / -ve sign are unsigned numbers.Numbers represented by sign magnitude are signednumbers.BCD represent as 4 bit binary code; also known as 8421code.Excess 3 code is obtained by addition of three Le. (0011)2to BCD and is setcomplementary,Gray codes are reflected codes in which the successivecoded characters differ in only bit position.Alphanumeric codes are represented by letters, symbolsand numbers. These are ABC codes, EBCDIC codes and ICIIcode.  Q 1. What is number system? What are its types? Giveexample for each type of number system. Ans. Number system : It is a set of rules and symbols, usedto represent number,’ The number system can be classifiedinto weighted. or positional and non-weighted or non-positional systems. Most of the number systems are of weighted type.The knowledge of number system is very essentialbecause the design and of a computer is dependent upon thenumber systems. Few important points related to numbersystem are: 1. Base or Radix: It is defined as the number of differentsymbols used in the number system. The number of valuesthat a character or digit can assume is called the Radix Base of the system. 2. The largest value of a digit is always less than theRadix or Base : If Radix r Base is. represented by ‘r’ or ‘b’,then the largest value of a digit is given by (r — 1) or (b — 1)For e.g. The largest digit in decimal number system is (10— 1) = 9. Where, 10 is the radix of decimal number system. Types of Number System : Following table shows thevarious, number system with their radix (r) or base (b).  Chapter 1 : Number System and Binary Code (Part 1) | Digital Electronicshttp://ptuece.loremate.com/die/node/12 of 121/11/2012 10:14 PM  1. The Decimal Number System : The number systemhaving radix or base ‘10’ called as decimal number system.The number which we make use in our life is called decimalnumber system.The decimal system has the base value of 10. So, itsmaximum or largest value of digit is (r — 1) = 10 — 1 = 9,where r = radix or base. Decimal position values as powers of 10 are as shown:  2. Binary Number System : The number system havingradix or base ‘2’ is called as binary number system.As the radix or base value of binary number system is ‘2’,so its maximum value of digit (r — 1) = (2— 1) = 1,where r is radixor base.The two binary digits are ‘1’ and ‘0’. in binary system eachbinary digit is known as bit and has its own weight or value.Its weight is expressed as a power of 2.  3. Octal Number System : The number system whichmake use of radix ‘8’ is known as octal number system. As theradix or base of octal number system is ‘8’, so its maximum orlargest value of a digit is(r — 1) = (8— 1) = 7 where r is radix or base.It make use of first eight digits of decimal number systemi.e. 0, 1, 2, 3, 4, 5, 6 and 7.Thus, 8 and 9 digits never come in octal number system.Octal positions values as a power of 8 are as shown: Chapter 1 : Number System and Binary Code (Part 1) | Digital Electronicshttp://ptuece.loremate.com/die/node/13 of 121/11/2012 10:14 PM    4. Hexadecimal Number System: The number systemhaving radix or base ‘16’ is called as hexadecimal numbersystem.. In short these are known as hex system’. Thenumber of values assumed by each digit are 0 through 9 andletters A, B, C, D, E and F. Thus the sixteen possible valuesare0, 1; 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F,Here ‘A’ represents 10 ‘B’ represents 1.1 ‘C’ represents 12 ‘D’ represents .13 ‘E’ represents 14 ‘F’ represents 15The largest value or maximum value for the ‘system is(r— 1) = (16 - 1) = 15 For e.g.  CONVERSION OF DIFFERENTNUMBERS (I) CONVERSION FROMBINARY TO DECIMAL   Q 1. Convert the binary number (110)2 to its decimalequivalent.  Chapter 1 : Number System and Binary Code (Part 1) | Digital Electronicshttp://ptuece.loremate.com/die/node/14 of 121/11/2012 10:14 PM
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