Conversion
In this number conversion tutorial we are learning to convert number between three commonly used number system, Binary, Octal and Hexadecimal.
In this tutorial we will see six examples: 1. Binary to Octal conversion 2. Octal to Binary conversion 3. Binary to Hexadecimal conversion 4. Hexadecimal to Binary conversion 5. Octal to Hexadecimal conversion 6. Hexadecimal to Octal conversion
Before we start lets talk a little about the number system that we are going to cover in this tutorial.
In decimal number system we use ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Decimal implies base 10.
In Binary number system we use two digits 0 and 1. Binary implies base 2.
In Octal number system we use eight digits 0, 1, 2, 3, 4, 5, 6 and 7. Octal implies base 8.
In hexadecimal number system we use ten digits and six english alphabet letters 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F. 10 is denoted as A 11 is denoted as B 12 is denoted as C 13 is denoted as D 14 is denoted as E 15 is denoted as F Hexadecimal implies base 16.
Following is the conversion table that we will use as a reference to perform conversion operations.
To convert a binary number into octal we follow the given steps 1. Divide the binary digits into groups of 3 digits, starting from the right. 2. Convert each group of 3 binary digits into 1 octal digit.
Step 1. Make groups of 3 digits from right 1001012 Groups: 1002 1012 Step 2. Convert each 3 digits group into 1 octal digit 1012 = 58 1002 = 48 so, 1001012 = 458
To convert an Octal number into Binary we follow the following steps 1. Convert each octal digits into 3 digits binary group 2. Combine the groups
Step 1. Convert each octal digit into 3 digits binary group 458 Groups: 48 58 58 = 1012 48 = 1002 Step 2. Combine the groups so, 458 = 1001012
To convert a binary number into hexadecimal we follow the given steps 1. Divide the binary digits into groups of 4 digits, starting from the right 2. Convert each group of 4 binary digits into 1 hexadecimal digit
Step 1. Make groups of 4 digits from right 101001012 Groups: 10102 01012 01012 = 516 10102 = 416 Step 2. Combine the groups so, 101001012 = 4516
To convert a hexadecimal number into binary we follow the given steps 1. Convert each hexadecimal digit into group of 4 digits binary 2. Combine the groups
Step 1. Convert each hexadecimal digit into group of 4 digits binary A516 Groups: A16 516 516 = 01012 A16 = 10102 Step 2. Combine the groups so, A516 = 101001012
To convert an octal number into hexadecimal we follow the given steps 1. Convert each octal digit into groups of 3 digits binary 2. Combine the groups from step 1 3. Divide the binary digits from step 2 into groups of 4 digits, starting from the right 4. Convert each group of 4 binary digits into 1 hexadecimal digit
Step 1. Convert each octal digit into groups of 3 digits binary 258 Groups: 28 58 58 = 1012 28 = 0102 Step 2. Combine the groups so, 258 = 0101012 Step 3. Divide the binary digits from step 2 into groups of 4 digits, starting from the right Groups: 00012 01012 Step 4. Convert each group of 4 binary digits into 1 hexadecimal digit 01012 = 516 00012 = 116 so, 258 = 1516
To convert a hexadecimal number into octal we follow the given steps 1. Convert each hexadecimal digit into groups of 4 digits binary 2. Combine the groups from step 1 3. Divide the binary digits from step 2 into groups of 3 digits, starting from the right 4. Convert each group of 3 binary digits into 1 octal digit
Step 1. Convert each hexadecimal digit into groups of 4 digits binary 1516 Groups: 116 516 516 = 01012 116 = 00012 Step 2. Combine the groups so, 1516 = 000101012 Step 3. Divide the binary digits from step 2 into groups of 3 digits, starting from the right Groups: 0002 0102 1012 Step 4. Convert each group of 3 binary digits into 1 octal digit 1012 = 58 0102 = 28 0002 = 08 so, 1516 = 0258 = 258