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DATA REPRESENTATION CONVERSION. NUMBER SYSTEM Decimal Number System Binary Number System Octal Number System Hexadecimal Number System.

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Presentation on theme: "DATA REPRESENTATION CONVERSION. NUMBER SYSTEM Decimal Number System Binary Number System Octal Number System Hexadecimal Number System."— Presentation transcript:

1 DATA REPRESENTATION CONVERSION

2 NUMBER SYSTEM Decimal Number System Binary Number System Octal Number System Hexadecimal Number System

3 Decimal Number System The 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

4 Binary Number System Binary 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.

5 Octal Number System The 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.

6 Hexadecimal 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.

7 NUMBER CONVERSIONS CONVERSIONS WITH BINARY Decimal To Binary Decimal Fraction To Binary Binary To Decimal Binary Fraction To Decimal

8 Decimal To Binary To 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 CONVERSIONS WITH BINARY WRITE IN THIS ORDER From Down to Up Your Answer =

9 Decimal Fraction To Binary To 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 Part Multiply(fractional part)0.375 * 2 = * 2 = * 2 = Your Answer is = Write From Up to Down CONVERSIONS WITH BINARY

10 Binary To Decimal To convert Binary to Decimal, Add positional weights or values with power of 2 start from right side. For Example Convert to Decimal * * * * * 2 0 = = (decimal) CONVERSIONS WITH BINARY

11 Binary Fraction To Decimal To 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 * * * * 2 -4 = = (decimal) CONVERSIONS WITH BINARY. 0101

12 NUMBER CONVERSIONS CONVERSIONS WITH OCTAL Decimal To Octal Decimal Fraction To Octal Octal To Decimal Octal To Binary Binary To Octal

13 Decimal To Octal A decimal integer can be converted to octal by repeated-division method with division factor of 8. Example Convert to Octal remainder = WRITE IN THIS ORDER From Down to Up CONVERSIONS WITH OCTAL

14 Decimal Fraction To Octal To convert Decimal fraction into Octal, multiply fractional part with 8 till you get fractional part 0. Example : convert to Octal Integer Part * 8 =  = CONVERSIONS WITH OCTAL Write From Up to Down

15 Octal To Decimal It can easily converted into decimal by multiplying each octal digit by its positional weight. For Example to Decimal * * * 8 0 = 3 * * * 1 = CONVERSIONS WITH OCTAL 372

16 Octal To Binary To 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 Table Example : to binary From table, 4 = 100, 7 = 111 & 2 = 010 We get = CONVERSIONS WITH OCTAL Octal Digit Binary

17 Binary To Octal Its simply the reverse of octal to binary. Make the three bits group starting from LSB. Then convert it with using Table For Example: to Octal Make group of three 011, 010 & = 3, 010 = 2 & 110 = = CONVERSIONS WITH OCTAL Octal Digit Binary Add Zero To Make it group of 3 bit.

18 NUMBER CONVERSIONS CONVERSIONS WITH HEX Decimal To HEX Decimal Fraction To HEX HEX To Decimal HEX To Binary Binary To HEX

19 Decimal To HEX A decimal integer can be converted to hex by repeated- division method with division factor of 16. Example Convert to Hex remainder A = 1A = A 16 WRITE IN THIS ORDER From Down to Up CONVERSIONS WITH HEX

20 Decimal Fraction To Hex To convert Decimal fraction into Hex, multiply fractional part with 16 till you get fractional part 0. Example : convert to Hex Integer Part * 16 = * 16 =  = CONVERSIONS WITH HEX Write From Up to Down

21 HEX To Decimal It can easily converted into decimal by multiplying each Hex digit by its positional weight has power of 16. For Example 2AF 16 to Decimal * A * F * 16 0 = 2 * * * 1 = CONVERSIONS WITH HEX 2AF DecimalHex DecimalHex A 11B 12C 13D 14E 15F

22 HEX To Binary To 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 Table Example : 3A6 16 to binary From table, 3 = 0011, A = 1010 & 6 = 0110 We get 3A6 16 = CONVERSIONS WITH HEX BinaryHex BinaryHex A 1011B 1100C 1101D 1110E 1111F

23 Binary To HEX Its simply the reverse of Hex to binary. Make the four bits group starting from LSB. Then convert it with using Table For Example: to Hex Make group of four 0010, 1011 & = 2, 1011 = B & 1010 = A = 2BA 16 CONVERSIONS WITH HEX Add Zero to Make it group of 4 bit. BinaryHex BinaryHex A 1011B 1100C 1101D 1110E 1111F

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