Number system

Number system

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  Number System Submitted to:Submitted by: Prof. Dr. A. K. Baliga Suraj Bora C.S.E(2061555)
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  What is NumberSystem ? •A system for representing number of certain type. •A number system defines a set of values used to represent quantity. • Example: –There are several systems for representing the counting numbers. –These include the usual base “10” or decimal system : 0,1,2,3,…..10,11,12,..99,100,…
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  Number System •Decimal isthe number system and is used in our day to day life •Binary is a number system that is used in computers •Octal is a number system that represents groups of binary numbers. It is used in digital displays. •Hexadecimal (Hex) is a number system that represents groups of binary numbers. Hex is primarily used in computing.
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  Different Number System •DecimalNumber System -Base 10 • Binary Number System - Base 2 • Octal Number System -Base 8 • Hexadecimal Number Sys tem - Base 16
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  Common Number System SystemBase Symbols Used by humans? Used in computers ? Decimal 10 0, 1, … 9 Yes No Binary 2 0, 1 No Yes Octal 8 0, 1, … 7 No No Hexa- decimal 16 0, 1, … 9, A, B, … F No No
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  Counting Decimal Binary Octal Hexa-decimal 0 0 0 0 1 1 1 1 2 10 2 2 3 11 3 3 4 100 4 4 5 101 5 5 6 110 6 6 7 111 7 7
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  Counting Decimal Binary Octal Hexa-decimal 8 1000 10 8 9 1001 11 9 10 1010 12 A 11 1011 13 B 12 1100 14 C 13 1101 15 D 14 1110 16 E 15 1111 17 F
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  Decimal Number System •Decimal number system contains ten unique symbols 0,1,2,3,4,5,6,7,8 and 9. • Since counting in decimal involves ten symbols, we can say that its base or radix is ten. • In this system, any number (integer, fraction or mixed) of any magnitude can be represented by the use of these ten symbols only • Each symbols in the number is called a “Digit” • Examples • 1214 • 1897 • 9875.54
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  Binary Number System •Binarynumber system is a positional weighted system. •It contains two unique symbols 0 and 1. •Since counting in binary involves two symbols , we can say that its base or radix is two. •A binary digit is called a “Bit” •A binary number consists of a sequence of bits, each of which is either a 0 or a 1. •The binary point separates the integer and fraction parts. •Examples, 1110 0000 1001 0101
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  Octal Number System •Octalnumber system is a positional weighted system. •It contains eight unique symbols 0,1,2,3,4,5,6 and 7. •Since counting in octal involves eight symbols, we can say that its base or radix is eight. •The largest value of a digit in the octal system will be 7. •That means the octal number higher than 7 will not be 8, instead of that it will be 10
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  Hexadecimal Number System •Binarynumbers are long. These numbers are fine for machines but are too lengthy to be handled by human beings. So there is a need to represent the binary numbers concisely. •One number system developed with this objective is the hexadecimal number system (or Hex) •It contains sixteen unique symbols •0,1,2,3,4,5,6,7,8,9,A,B,C,D,E and F. •Since counting in hex involves sixteen symbols, we can say that its base or radix is sixteen.
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  BCD or 8421Numbers •BCD means Binary Coded Decimal. •BCD is a system of weiting a numbers that a four-digit binary code to each digit 0 through 9 in decimal numbers. •The smallest BCD number is (0000) and the largest is (1001). The next number to 9 will be 10 which is expressed as (0001 0000) in BCD. •There are six illegal combinations 1010, 1011,1100, 1101, 1110 and 1111 in this code i.e. they are not part of the 8421 BCD code
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  Decimal to BCDconversion Sr.No. Decimal Number BCD 1 2 0010 2 11 00010001 3 6 0110 4 213 001000010011 5 10 0001000
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  Gray Code(non weightedbinary code) • The gray code is non-weighted code. • It is not suitable for arithmetic operations. • It is a cyclic code i.e. unit distance code • PROPERTIES OF GRAY CODE 1.Unit Distance Code successive code words in this code differ in one bit position only. 2.Reflective Code grey codes for all decimal numbers can be generated through the reflective property through the table.
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  Gray Code(non weightedbinary code)
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  Excess-3 Code • Theexcess-3 is non-weighted BCD code. • This code derives its name from the fact that each binary code word is the corresponding 8421 code word plus 0011. • It is a sequential code & therefore can be used for arithmetic operations. • It is a self complementing code