# Computer Number Conversion - Computer Fundamentals

## What is Number Conversion?

There are many methods or techniques where the computer uses in its language for performing specific tasks. It can be used to convert numbers from one base to another. In this chapter, we'll demonstrate the following −
• Decimal to Other Base System
• Other Base System to Decimal
• Other Base System to Non-Decimal
• Shortcut method - Binary to Octal
• Shortcut method - Octal to Binary
• Shortcut method - Binary to Hexadecimal
• Shortcut method - Hexadecimal to Binary

## Decimal to Other Base System

Step 1 − Divide the decimal number that is to be converted with the value of the new base.
Step 2 − Get the remainder from Step 1 as the rightmost digit (least significant digit) of the new base number.
Step 3 − Divide the quotient of the previous one divide by the new base.
Step 4 − Place the remainder from Step 3 as the next digit (to the left) 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

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 – The column values that are obtained should multiply (in Step 1) by the digits in the corresponding columns.
Step 3 − Sum the products calculated in Step 2. The total is the equivalent value in decimal.

## Example

Binary Number:111012
Calculating Decimal Equivalent −
Step Binary Number Decimal Number
Step 1 111012 ((1 x 24) + (1 x 23) + (1 x 22) + (0 x 21) + (1 x 20))10
Step 2 111012 (16 + 8 + 4 + 0 + 1)10
Step 3 111012 2910
Binary Number :111012= Decimal Number :2910

## Other Base System to Non-Decimal System

Step 1 − Convert the original number to a decimal number (base 10).
Step 2 − Convert the decimal number so obtained to the new base number.

## Example

Octal Number :258
Calculating Binary Equivalent −
Step 1 - Convert to Decimal
StepOctal NumberDecimal Number
Step Octal Number Decimal Number
Step 1 258 ((2 x 81) + (5 x 80))10
Step 2 258 (16 + 5)10
Step 3 258 2110
Octal Number :258= Decimal Number :2110
Step 2 - Convert Decimal to Binary
StepOperationResultRemainder
Step Operation Result Remainder
Step 1 21 / 2 10 1
Step 2 10 / 2 5 0
Step 3 5 / 2 2 1
Step 4 2 / 2 1 0
Step 5 1 / 2 0 1
Decimal Number :2110= Binary Number :101012
Octal Number :258= Binary Number :101012

## Shortcut Method ─ Binary to Octal

Step 1 − Divide the binary digits into groups of three (starting from the right).
Step 2 − Convert each group of three binary digits to one octal digit.

## Example

Binary Number :101012
Calculating Octal Equivalent −
StepBinary NumberOctal Number
Step Binary Number Octal Number
Step 1 101012 010 101
Step 2 101012 2858
Step 3 101012 258
Binary Number :101012= Octal Number :258

## Shortcut Method ─ Octal to Binary

Step 1 − Convert each octal digit to a 3-digit binary number (the octal digits may be treated as decimal for this conversion).
Step 2 − Combine all the resulting binary groups (of 3 digits each) into a single binary number.

## Example

Octal Number :258
Calculating Binary Equivalent −
StepOctal NumberBinary Number
Step Octal Number Binary Number
Step 1 258 210510
Step 2 258 01021012
Step 3 258 0101012
Octal Number :258= Binary Number :101012

## Shortcut Method ─ Binary to Hexadecimal

Step 1 − Divide the binary digits into groups of four (starting from the right).
Step 2 − Convert each group of four binary digits to one hexadecimal symbol.

## Example

Binary Number :101012
Step 1 101012 0001 0101
Step 2 101012 110510
Step 3 101012 1516
Binary Number :101012= Hexadecimal Number :1516

## Shortcut Method - Hexadecimal to Binary

Step 1 − Convert each hexadecimal digit to a 4-digit binary number (the hexadecimal digits may be treated as decimal for this conversion).
Step 2 − Combine all the resulting binary groups (of 4 digits each) into a single binary number.