How we represent decimal number into hexadecimal

9514 1404 393

Explanation:

In base 10, the digits we use to represent numbers are 0 to 9. Each location in a base-10 number has a place-value. That is, the value of the digit is dependent upon its place in the number.

Any number in base 10 can be written in expanded form like this:

  8765.432

  = 8·10³ +7·10² +6·10¹ +5·10⁰ +4·10⁻¹ +3·10⁻² +2·10⁻³

We hope you recognize that in this form, the place value of a digit is a power of the base, and that those powers increase to the left and decrease to the right. The "units" place has a power of 0.

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Hexadecimal works the same way. In that base-16 number system, the digits 0-9 and A-F are used. The corresponding decimal values are ...

  A = 10, B = 11, C = 12, D = 13, E = 14, F = 15

As above, an expanded hexadecimal number would use powers of the number system base:

  A73B.16E

  = 10·16³ +7·16² +3·16¹ +11·16⁰ +1·16⁻¹ +6·16⁻² +14·16⁻³ . . . (all numbers decimal)

The method of converting a number from hexadecimal is generally to evaluate the expanded form, as just shown. (The base-10 value of the number shown is 42,811.08935546875.)

There are a number of methods for converting numbers to hexadecimal. For integers, one can work right to left, with each successive digit of the hex number being the remainder from division by 16. The quotient is then used for developing further digits to the left.

Example:

  9243/16 = 577 11/16

  577/16 = 36 1/16

  36/16 = 2 4/16

  9243₁₀ = 241B₁₆

In the above, we have identified the base of the numbers being used with a subscript. If the base is understood, that is unnecessary. (However, it is useful in ambiguous cases.)

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Some calculators have modes for converting and/or calculating with hexadecimal integers. They are generally limited to 48 bits (12 hex digits) or less. I have not seen any that convert or calculate fractions in non-decimal bases. There may be apps or web products that will do fraction conversion—generally for the purpose of showing you the IEEE-754 representation used internally by digital computers.

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