Report

DATA REPRESENTATION CONVERSION NUMBER SYSTEM Decimal Number System Binary Number System Octal Number System Hexadecimal Number System 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 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. 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. 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. NUMBER CONVERSIONS CONVERSIONS WITH BINARY Decimal To Binary Decimal Fraction To Binary Binary To Decimal Binary Fraction To Decimal CONVERSIONS WITH BINARY 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 4310 2 2 2 2 2 2 43 21 10 5 2 1 1 1 1 0 1 0 1 WRITE IN THIS ORDER From Down to Up Your Answer 4310 = 101011 2 CONVERSIONS WITH BINARY 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 0.37510 to Binary Integer Part Multiply(fractional part)0.375 * 2 = 0.750 0 Write 0.75 * 2 = 1.50 1 From Up to 0.50 * 2 = 1.00 1 Down Your Answer is 0.37510 = 0.0112 CONVERSIONS WITH BINARY Binary To Decimal To convert Binary to Decimal, Add positional weights or values with power of 2 start from right side. For Example Convert 11011 to Decimal. 1 24 1 0 22 1 21 1 20 23 1 * 24 + 1 * 23 + 0 * 22 + 1 * 21 + 1 * 20 = 16 + 8 + 0 + 2 + 1 = 2710 (decimal) CONVERSIONS WITH BINARY 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 0.0101 to Decimal. . 0 2-1 1 0 2-3 2-2 0 * 2-1 + 1 * 2-2 + 0 * 2-3 + 1 * 2-4 = 0 + 0.25 + 0 + 0.0625 0.01012 = 0.312510 (decimal) 1 2-4 NUMBER CONVERSIONS CONVERSIONS WITH OCTAL Decimal To Octal Decimal Fraction To Octal Octal To Decimal Octal To Binary Binary To Octal CONVERSIONS WITH OCTAL Decimal To Octal A decimal integer can be converted to octal by repeated-division method with division factor of 8. Example Convert 26610 to Octal remainder 8 8 8 266 33 4 0 2 1 4 WRITE IN THIS ORDER From Down to Up 26610 = 4128 CONVERSIONS WITH OCTAL Decimal Fraction To Octal To convert Decimal fraction into Octal, multiply fractional part with 8 till you get fractional part 0. Example : convert 0.37510 to Octal Integer Part Write 0.375 * 8 = 3.0 3 From 0.37510 = 0.38 Up to Down CONVERSIONS WITH OCTAL Octal To Decimal It can easily converted into decimal by multiplying each octal digit by its positional weight. For Example 3728 to Decimal 3 82 7 81 3 * 82 + 7 * 81 + 2 * 80 = 3 * 64 + 7 * 8 + 2 * 1 = 25010 2 80 CONVERSIONS WITH OCTAL 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 Octal Digit 0 1 2 3 4 5 6 7 Binary 000 001 010 011 100 101 110 111 Example : 4728 to binary From table , 4 = 100 , 7 = 111 & 2 = 010 We get 4728 = 1001110102 CONVERSIONS WITH OCTAL 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 Octal Digit 0 1 2 3 4 5 6 7 Binary 000 001 010 011 100 101 110 111 For Example: 110101102 to Octal Make group of three 011 , 010 & 110 011 = 3 , 010 = 2 & 110 = 6 110101102 = 3268 Add Zero To Make it group of 3 bit. NUMBER CONVERSIONS CONVERSIONS WITH HEX Decimal To HEX Decimal Fraction To HEX HEX To Decimal HEX To Binary Binary To HEX CONVERSIONS WITH HEX Decimal To HEX A decimal integer can be converted to hex by repeated- division method with division factor of 16. Example Convert 26610 to Hex remainder 16 16 16 423 26 1 0 7 A 1 1010 = A16 WRITE IN THIS ORDER From Down to Up 42310 = 1A716 CONVERSIONS WITH HEX Decimal Fraction To Hex To convert Decimal fraction into Hex, multiply fractional part with 16 till you get fractional part 0. Example : convert 0.0312510 to Hex Integer Part Write 0. 03125 * 16 =0.5 0 From Up to 0. 5 * 16 = 8.0 8 Down 0.0312510 = 0.0816 CONVERSIONS WITH HEX HEX To Decimal It can easily converted into decimal by multiplying each Hex digit by its positional weight has power of 16. For Example 2AF16 to Decimal Decimal Hex 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 2 162 A F 161 160 2 * 162 + A * 161 + F * 160 = 2 * 256 + 10 * 8 + 15 * 1 = 60710 Decimal Hex 8 8 9 9 10 A 11 B 12 C 13 D 14 E 15 F CONVERSIONS WITH HEX 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 Binary Binary Hex Hex 1000 8 1001 9 1010 A 1011 B 1100 C 5 1101 D 0110 6 1110 E 0111 7 1111 F 0000 0 0001 1 0010 2 0011 3 0100 4 0101 Example : 3A616 to binary From table, 3 = 0011 , A = 1010 & 6 = 0110 We get 3A616 = 0011101001102 CONVERSIONS WITH HEX 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 Add Zero to Make it Binary Hex group of 4 bit. Binary Hex 1000 8 1001 9 1010 A 1011 B 1100 C 1101 D 6 1110 E 7 1111 F 0000 0 0001 1 0010 2 0011 3 0100 4 0101 5 0110 0111 For Example: 10101110102 to Hex Make group of four 0010 , 1011 & 1010 0010 = 2 , 1011 = B & 1010 = A 10101110102 = 2BA16