Convert from binary (with floating point) to decimal?

Question

I have to convert the number (111011,01) in binary (2) to decimal (10). I looked up many guides on YouTube but none really explained how it's done, or it's very hard to hear. I would appreciate if someone can explain to me step by step how can I do it. Thank you.

Answer 1

The 1 that is immediately left of the binary point (,) is the unit column and has the value 1. Every other 1 is worth twice as much for each place it is to the left of the unit column, or half as much for each place it is to the right of the unit column.

$$\def\one#1{\color{#1}{1}} \one{darkred} \one{red} \one{orange} 0 \one{blue} \one{lightblue} ,0 \one{green} = \\ \color{darkred}{32} + \color{red}{16} + \color{orange}{8} + 0 +\color{blue}{2} + \color{lightblue}{1} + 0 + \color{green}{\frac14} = 59\frac14. $$

(Also, that is not a floating-point number. It is a fixed-point number.)

Answer 2

Here's a website which can help you understand how it works.

If you just want to know how much it is I suggest using Wolfram Alpha.

In your case it is $59.25$.