Hexadecimal Number System

The hexadecimal system is a base-16 number system that plays an important role in computing and digital systems. It uses sixteen symbols to represent values:

Digits (0 to 9) and the letters A to F, where A = 10, B = 11, and so on up to F = 15.

Place Value of Digits

The numbers in the hexadecimal number system have weightage in powers of 16. The power of 16 increases as the digit is shifted towards the left of the number. This is explained by the example as,

Example: (AB12)₁₆

Place value of each digit in (AB12)₁₆ is,

= A×16³ + B×16² + 1×16¹ + 2×16⁰

Conversions

Conversion of a number system means conversion from one base to another. The following are the conversions of the Hexadecimal Number System to other Number Systems:

Hexadecimal to Decimal Conversion

To convert a hexadecimal number to decimal (base-10), multiply each digit by its corresponding power of 16 and sum the results.

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

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 multiplication and the final sum will be the decimal number.

Hexadecimal to Binary Conversion

Each hexadecimal digit corresponds to a 4-bit binary sequence. Convert each digit individually and combine.

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

Follow the steps given below:

• Step 1: Convert the Hex symbols into their 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.

Hexadecimal to Octal Conversion

Convert hexadecimal to binary, group the binary digits into sets of three (right to left), and convert each group to its octal equivalent.

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

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 an 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 before MSB to make it a proper group of three digits(if required)
• Step 4: Now convert these groups into their relevant decimal values.

Decimal to Hexadecimal Conversion

Divide the decimal number by 16 repeatedly, noting remainders, until the quotient is 0. Read remainders in reverse order, using A–F for 10–15.

➢Practice: Solved Examples