Conversion from Hexadecimal to Other Number Systems

Hex Numbers are represented with digits 0-9 and with letters A-F and with base 16. Conversion of a number system means conversion from one base to another. Following are the conversions of the Hexadecimal Number System to other Number Systems:

Hexadecimal to Decimal Conversion: 

Hexadecimal numbers are represented in base 16 but the decimal numbers are of base 10. Hence, to convert a hexadecimal number to a decimal number, the base of that number is to be changed. Follow the steps given below:

• Step 1: Write the decimal values of the symbols used in the Hex number i.e. from A-F
• Step 2: Multiply each digit of the Hex number with its place value. starting from right to left i.e. LSB to MSB.
• Step 3: Add the result of multiplications and the final sum will be the decimal number.

Example: To convert (8EB4)₁₆ into a decimal value

Hexadecimal to Binary Conversion

Hex numbers are represented in base 16, but the binary numbers are of base 2. Hence, to convert a hexadecimal number to a binary number, the base of that number is to be changed. Follow the steps given below:

• Step 1: Convert the Hex symbols into its equivalent decimal values.
• Step 2: Write each digit of the Hexadecimal number separately.
• Step 3: Convert each digit into an equivalent group of four binary digits.
• Step 4: Combine these groups to form the whole binary number.

Example: (B2E)₁₆ is to be converted to binary

Hexadecimal to Octal Conversion:

Hexadecimal numbers are represented in base 16, but the octal numbers are of base 8. Hence, to convert a hex number to an octal number, the base of that number is to be changed. Follow the steps given below:

• Step 1: We need to convert the Hexadecimal number to Binary first. For that, follow the steps given in the above conversion.
• Step 2: Now to convert the binary number to Octal number, divide the binary digits into groups of three digits starting from right to left i.e. from LSB to MSB. 
• Step 3: Add zeros prior to MSB to make it a proper group of three digits(if required)
• Step 4: Now convert these groups into their relevant decimal values.

Example: (B2E)₁₆ is to be converted to hex

Read More:

• Numbers
• Positive and Negative Numbers
• Whole Numbers
• Prime Numbers
• Composite Numbers

Number System is a method of representing numbers on the number line with the help of a set of Symbols and rules. These symbols range from 0-9 and are termed as digits. Let’s learn about the number system in detail, including its types, and conversion.