2NUMBER SYSTEMDecimal Number SystemBinary Number SystemOctal Number SystemHexadecimal Number System
3Decimal Number SystemThe decimal system is composed of 1- numerals or symbols (Deca means 10, that is why this is called decimal system). These 10 symbols are 0,1,2,3,4,5,6,7,8,9 ; using these symbols as digit as number, we can express any quantity. The decimal system, also called the base-10 system
4Binary Number SystemBinary System, there are only two symbols or possible digit values, 0 and 1. This base-2 system can be used to represent any quantity that can be represented in decimal or other number systems.The Binary system is also a positional-value system, wherein each binary digit has its own value expressed as a power of 2.
5Octal Number SystemThe Octal number system is very important in digital computer work. The octal number system has a base of eight, meaning that it has eight unique symbols : 0,1,2,3,4,5,6,7 . Thus each digit of an octal number can have any value from 0 to 7.The octal system is a positional value system, wherein each octal digit has its own value expressed as a power of 8.
6Hexadecimal Number System The Hexadecimal System uses base 16. Thus, it has 16 possible digit symbols. It uses the digits 0 – 9 and the letter A, B, C, D, E & F as the 16 digit symbols.Hexadecimal is a positional value System has its own value expressed as a power of 16.
7NUMBER CONVERSIONSCONVERSIONS WITH BINARYDecimal To BinaryDecimal Fraction To BinaryBinary To DecimalBinary Fraction To Decimal
8CONVERSIONS WITH BINARY Decimal To BinaryTo converting decimal to Binary we use Repeated division method. In this the no. is successively divide by 2 and its remainder recorded.For Example convert decimal to Binary 4310WRITE INTHIS ORDERFrom Down to UpYour Answer =
9Decimal Fraction To Binary CONVERSIONS WITH BINARYDecimal Fraction To BinaryTo Convert a decimal fraction into binary, multiply the decimal fraction by the base that’s 2. Do untill you will get zero at fractional part.For Example Convert to Binary Integer PartMultiply(fractional part)0.375 * 2 =0.75 * 2 =0.50 * 2 =Your Answer is =WriteFromUp toDown
10CONVERSIONS WITH BINARY Binary To DecimalTo convert Binary to Decimal, Add positional weights or values with power of 2 start from right side.For Example Convert to Decimal.1 * * * * * 20== 2710 (decimal)1
11Binary Fraction To Decimal CONVERSIONS WITH BINARYBinary Fraction To DecimalTo find binary fraction, take the sum of products of each digit value (0 – 1) and its positional value. Starts from left side.For Example convert to Decimal.0 * * * * 2-4== (decimal)1
12NUMBER CONVERSIONSCONVERSIONS WITH OCTALDecimal To OctalDecimal Fraction To OctalOctal To DecimalOctal To BinaryBinary To Octal
13CONVERSIONS WITH OCTAL Decimal To OctalA decimal integer can be converted to octal by repeated-division method with division factor of 8.Example Convert to Octalremainder26610 = 4128WRITE INTHIS ORDERFrom Down to Up
14Decimal Fraction To Octal CONVERSIONS WITH OCTALDecimal Fraction To OctalTo convert Decimal fraction into Octal, multiply fractional part with 8 till you get fractional part 0.Example : convert to OctalInteger Part0.375 * 8 = = 0.38WriteFromUp toDown
15CONVERSIONS WITH OCTAL Octal To DecimalIt can easily converted into decimal by multiplying each octal digit by its positional weight.For Example 3728 to Decimal3 * * * 80= 3 * * * 1= 25010372
16CONVERSIONS WITH OCTAL Octal To BinaryTo convert Octal To Binary is easy. This converting is performed by converting each octal digit to its 3 bit binary. Possible digits converted as indicated in TableExample : 4728 to binaryFrom table , 4 = 100 , 7 = 111 & 2 = 010We get 4728 =Octal Digit1234567Binary000001010011100101110111
17CONVERSIONS WITH OCTAL Binary To OctalIts simply the reverse of octal to binary. Make the three bits group starting from LSB. Then convert it with using TableFor Example: to OctalMake group of three 011 , 010 & 110011 = 3 , 010 = 2 & 110 = 6= 3268Octal Digit1234567Binary000001010011100101110111Add ZeroTo Make it group of3 bit.
18NUMBER CONVERSIONSCONVERSIONS WITH HEXDecimal To HEXDecimal Fraction To HEXHEX To DecimalHEX To BinaryBinary To HEX
19CONVERSIONS WITH HEXDecimal To HEXA decimal integer can be converted to hex by repeated-division method with division factor of 16.Example Convert to HexremainderA42310 = 1A7161010 = A16WRITE INTHIS ORDERFrom Down to Up
20Decimal Fraction To Hex CONVERSIONS WITH HEXDecimal Fraction To HexTo convert Decimal fraction into Hex, multiply fractional part with 16 till you get fractional part 0.Example : convert to HexInteger Part* 16 =0. 5 * 16 = =WriteFromUp toDown
21CONVERSIONS WITH HEXHEX To DecimalIt can easily converted into decimal by multiplying each Hex digit by its positional weight has power of 16.For Example 2AF16 to Decimal2 * A * F * 160= 2 * * * 1= 60710DecimalHex1234567DecimalHex8910A11B12C13D14E15F2AF
22CONVERSIONS WITH HEXHEX To BinaryTo convert Hex To Binary is easy. This converting is performed by converting each hex digit to its 4 bit binary. Possible digits converted as indicated in TableExample : 3A616 to binaryFrom table, 3 = 0011 ,A = & 6 = 0110We get 3A616 =BinaryHex000000011001020011301004010150110601117BinaryHex10008100191010A1011B1100C1101D1110E1111F
23CONVERSIONS WITH HEXBinary To HEXIts simply the reverse of Hex to binary. Make the four bits group starting from LSB. Then convert it with using TableFor Example: to HexMake group of four 0010, & 10100010 = 2 , 1011 = B & 1010 = A= 2BA16Add Zero to Make it group of 4 bit.BinaryHex000000011001020011301004010150110601117BinaryHex10008100191010A1011B1100C1101D1110E1111F