K.S.V.M EDUCATION CENRE NAME HARSH PATEL SUBMITTED TO, ARVIND SIR CLASS IX TH ROLL NO 06
Welcom e t o Computer Presentation……
INTRODUTION WHAT IS COMPUTER ? A Computer is an electronic machine that can solve different problems , process Data, store & retrieve data and perform calculation faster and efficiently than humans ….
NUMBER SYSTEM The technique to represent and work with numbers is called NUMBER SYSTEM. Decimal number system is the most common number system . Other popular number systems include binary number system, octal number system, hexadecimal number system, etc .….
Hexadecimal NUMBER WHAT IS HEXADECIMAL ? Hexadecimal number system has 16 symbols --- 0 to 9 and A and is equal to m10, B is equal to 11 and so on till F . Hexadecimal number system is also a positional value system with where each digit has its value expressed in powers of, as shown here: 16 5 16 4 16 3 16 2 16 1 16 27FB 16 = 2 * 16 3 + 7 * 16 2 + 15 * 16 1 + 10 * 16 = 8192 + 1792 + 240 + 10 = 10234 10
Octal decimal NUMBER WHAT IS OCTAL DECIMAL ? Octal number system has eight digits 0, 1, 2, 3, 4, 5, 6 and 7 . Octal number system is also a positional value system with where each digit has its value expressed in powers of 8, as shown here : 8 5 8 4 8 3 8 2 8 1 8 726 8 = 7 * 8 2 + 2 * 8 1 + 6 * 8 = 448 + 16 + 6 = 470 10
Hexadecimal to octal conversion
Conversion of hexadecimal to octal cannot be done directly. Firstly we need to convert hexadecimal into its equivalent decimal number then decimal to octal. Follow the steps below to understand the process. Consider the given hexadecimal number First count the number of digits in the number If n is the position of the digit from the right end then multiply each digit with 16 n-1 Add the terms after multiplication Resultant is the equivalent decimal form Divide the decimal number with 8 Note down the remainder Repeat the previous two steps with the quotient, until the quotient is zero Write the remainders in reverse order The obtained number is the required result
Some example Find the equivalent octal form of C1 1 6 . Solution: Given, a hexadecimal number is C1 C1 16 = (C × 16 1 ) + (1 × 16 ) = C × 16 + 1 × 1 =12 × 16 + 1 = 192 + 1 C1 16 =193 (Decimal form) Now we have to convert this decimal to octal number; The octal number is 301 8 Hence, C1 16 = 301 8
octal to hexadecimal conversion
The simplest way is to convert the octal number into a decimal, then the decimal into hexadecimal form. Write the powers of 8 (1, 8, 64, 512, 4096, and so on) beside the octal digits from bottom to top. Multiply each digit by its power. Add up the answers. This is the decimal solution. Divide the decimal number by 16. Get the integer quotient for the next iteration (if the number will not divide equally by 16, then round down the result to the nearest whole number). Keep a note of the remainder, it should be between 0 and 15. Repeat the steps from step 4. Until the quotient is equal to 0. Write out all the remainders, from bottom to top. Convert any remainders bigger than 9 into hex letters. This is the hex solution.
Convert 536 from octal to hexadecimal number. Convert 536(octal) into its binary equivalent we get (536) 8 = (101) (011) (110) =(101011110) 2 Now forming the group of 4 binary bits to obtain its hexadecimal equivalent, (101011110) 2 = (0001) (0101) (1110) = (15E) 16 So the hexadecimal number of 536 is 15E. Solution: Some example