Number System - Introduction to information technology

NUMBER SYSTEM CONVERSION

There are many methods or techniques which can be used to convert numbers from one base to
another. We'll demonstrate here the following −
1-Decimal to Other Base System
2-Other Base System to Decimal
3-Other Base System to Non-Decimal
4-Shortcut method − Binary to Octal
5-Shortcut method − Octal to Binary
6-Shortcut method − Binary to Hexadecimal
7-Shortcut method − Hexadecimal to Binary

Decimal to Other Base System

Step 1 − Divide the decimal number to be converted by the value of the new base.

Step 2 − Get the remainder from Step 1 as the rightmost digit leastsignificantdigit of new base number.

Step 3 − Divide the quotient of the previous divide by the new base.

Step 4 − Record the remainder from Step 3 as the next digit totheleft of the new base

number.

Repeat Steps 3 and 4, getting remainders from right to left, until the quotient becomes zero in Step

3.

The last remainder thus obtained will be the Most Significant Digit MSD of the new base number.

Example:−

Decimal Number: 2910

Calculating Binary Equivalent

Step                    Operation                        Result                 Remainder

Step 1                  29 / 2                          14                       1

Step 2                  14 / 2                           7                        0

Step 3                     7 / 2                          3                        1

Step 4                     3 / 2                          1                        1  

Step 5                     1 / 2                           0                       1

As mentioned in Steps 2 and 4, the remainders have to be arranged in the reverse order so that

the first remainder becomes the Least Significant Digit LSD and the last remainder becomes the

Most Significant Digit MSD.

Decimal Number − 2910 = Binary Number − 111012

Other Base System to Decimal System

Steps

Step 1 − Determine the column positional value of each digit 

this depends on the position of the digit and the base of the number system.

Step 2 − Multiply the obtained column values inStep1 by the digits in the corresponding 

columns.

Step 3 − Sum the products calculated in Step 2. The total is the equivalent value in decimal

Other Base System to Non-Decimal System

Steps

Step 1 − Convert the original number to a decimal number base10.

Step 2 − Convert the decimal number so obtained to the new base number.

Shortcut method - Binary to Octal

Steps

Step 1 − Divide the binary digits into groups of three startingfromtheright.

Step 2 − Convert each group of three binary digits to one octal digit

Example:-

Binary Number − 101012

Calculating Octal Equivalent −

Step           Binary Number              Octal Number

Step 1           101012                            010 101

Step 2           101012                              28 58

Step 3           101012                                258

Binary Number − 101012 = Octal Number − 258