Hexa-decimal Number System

The hexa-decimal number system has a radix or base 16. It requires 16 symbols to represent a number in this system. The symbols are 0 to 9, A, B, C, D, E, F where the symbols A, B, C, D, E, F represent the decimal numbers 10, 11, 12, 13, 14, 15 respectively. Let us recall the conversion table for the decimal numbers 0 to 15 and their binary, octal and hexa-decimal equivalents.

The conversion of hexa-decimal numbers to their decimal equivalents is straight-forward and follows the same rules as that of octal or binary to decimal. Similarly, conversion of decimal to hexa-decimal may be worked out with the help of division or multiplication, as the case may be, by the radix 16.

The example on hexa-decimal number system will help us to understand the procedure:

1. Convert B6A₁₆ to its decimal equivalent.



Solution:

B6A₁₆

= 11 × 16² + 6 × 16¹ + 10 × 16⁰

= 2816 + 96 + 10

= 2922₁₀

Therefore, B6A₁₆ = 2922₁₀


2. Convert 3917₁₀ to its hexa-decimal equivalent

Solution:

3917₁₀
Therefore, 3917₁₀ = F4D₁₆

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● Binary Numbers

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• Number System

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• Why Binary Numbers are Used

• Binary to Decimal Conversion

• Conversion of Numbers

• Octal Number System

• Hexa-decimal Number System

• Conversion of Binary Numbers to Octal or Hexa-decimal Numbers

• Octal and Hexa-Decimal Numbers

• Signed-magnitude Representation

• Radix Complement

• Diminished Radix Complement

• Arithmetic Operations of Binary Numbers

• Binary Addition

• Binary Subtraction

• Subtraction by 2’s Complement

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• Addition and Subtraction of Binary Numbers

• Binary Addition using 1’s Complement

• Binary Addition using 2’s Complement

• Binary Multiplication

• Binary Division

• Addition and Subtraction of Octal Numbers

• Multiplication of Octal Numbers

• Hexadecimal Addition and Subtraction

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