How to decode user options

[Andreas]

OK, let's start at 0
Computers can only handle two signal states: Low and High (Voltage).
This represents a Bit, eg. 0 or 1.
All Numbers are constructed as a series of bits, for example 01101001.
This is called the binary or dual system, in opposite to the decimal system we use for everyday calculations.
As there are only 2 Values (0 and 1), the base for this is 2.
How do we determine the value of a number in the decimal system:
For eamle 126 is One Hundred and Twenytsix, or One Hundred + Tweny + Six, or formally:
6*10^0 + 2*10^2 + 1*10^2
This works the same way in dual system, but with 2 as base:
10000 = 0*2^0 + 0*2^1 + 0*2^2 + 0*2^3 + 0*2^4 = 16

As you can see, 16 represents the 5th bit.

Now we got some decimal number, let's say 287654.

How do we know if the 5th bit is set?
First we convert this to a number in dual system by cintinued division:

287654 / 2 = 143827 + 0
143827 / 2 = 71913  + 1
71913  / 2 = 35956  + 1
35956 / 2 = 17978   + 0
17978 / 2 = 8989    + 0
8989 / 2 = 4494     + 1
4494 / 2 = 2247     + 0
2247 / 2 = 1123     + 1
1123 / 2 = 561      + 1
561 / 2 = 280       + 1
280 / 2 = 140       + 0
140 / 2 = 70        + 0
70 / 2 = 35         + 0
35 / 2 = 17         + 1
17 / 2 = 8          + 1
8 / 2 = 4           + 0
4 / 2 = 2           + 0
2 / 2 = 1           + 0
1 / 2 = 0           + 1

Now we write down the remaining values in reversed order:

1000110001110100110

This is decimal 287654 in dual system.

Now we can check if bit #5 (decimal 16, dual 10000) is set:

1000110001110100110
              10000

Technically, this is a AND operation. Every bit position is compared - if both are the same the result-bit at this position is 1:

  1000110001110100110
&               10000
= 0000000000000000000

As the can see, the result is 0.

But if we had for example

  1000110001110110110
&               10000
= 0000000000000010000

Here the result is not 0, eg. the bit is set.
What is the difference between 1000110001110100110 and 1000110001110110110?

We already know that 1000110001110100110 is 287654 because we started with this.
So let's convert 1000110001110110110 to decimal:

0*2^0 + 1*2^1 + 1*2^1 + 0*2^2 ... = 287670.

As you can see, the difference is 16, as expected as this represents the bit we just set.

Maybe this makes things a bit clearer - or got you totally confused