Radix Point - Examples

Examples

  • In base 10 (decimal): 13.625
In this example, 13 is the integer to the left of the radix point, and 625 (i.e. 625/1000) is the fractional part to the right.
  • In base 2 (binary): 1101.101
The binary number 1101.101 has the following digits:
Power of 2 3 2 1 0 −1 −2 −3
Binary digit 1 1 0 1 . 1 0 1

Hence, its decimal value can be calculated as:

\begin{align} 1101.101_2 &= 1 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 + 1 \times 2^{-1} + 0 \times 2^{-2} + 1 \times 2^{-3} \\ &= 1 \times 8 + 1 \times 4 + 0 \times 2 + 1 \times 1 + 1 \times 0.5 + 0 \times 0.25 + 1 \times 0.125 \\ &= 8 + 4 + 0 + 1 + 0.5 + 0 + 0.125 \\ &= 13.625_{10} \end{align}

It is now seen that 1101, which is to the left of the radix point, is the binary representation of the decimal number 13. To the right of the radix point is 101, which is the binary representation of the decimal fraction 625/1000 (or 5/8).

Read more about this topic:  Radix Point

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