Shortcut methods For Number System Conversion

There Are many methods to convert number system to other number System here there are few shortcuts methods to covert one number system to another number system   

1. Binary to Octal
2. Octal to Binary
3. Binary to Hexadecimal
4. Hexadecimal to Binary

1. Binary to Octal

Steps

1.  Divide the binary digits into groups of three (starting from the right).
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

2. Octal to Binary

Steps

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

Example

Octal Number  25₈

Calculating Binary Equivalent 

Step	Octal Number	Binary Number
Step 1	258	210 510
Step 2	258	0102 1012
Step 3	258	0101012

Octal Number 25₈ = Binary Number 10101₂

3. Binary to Hexadecimal

Steps

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

Example

Binary Number  10101₂

Calculating hexadecimal Equivalent 

Step	Binary Number	Hexadecimal Number
Step 1	101012	0001 0101
Step 2	101012	110 510
Step 3	101012	1516

Binary Number  10101₂ = Hexadecimal Number  15₁₆

4. Hexadecimal to Binary

Steps

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

Example

Hexadecimal Number − 15₁₆

Calculating Binary Equivalent −

Step	Hexadecimal Number	Binary Number
Step 1	1516	110 510
Step 2	1516	00012 01012
Step 3	1516	000101012

Hexadecimal Number  15₁₆ = Binary Number 10101₂