Convert Hexadecimal to Binary number I would like to know how to convert a Hexadecimal lets say 3BF to the binary format in a calculational way. (Not the comparing with tables)
It would be great to have a step by step guide how the 1110111111 result is produced.
 A: Convert every digit to a four-digit binary number and concatenate.
$3=(0011)_2, B=(11)_{10}=(1011)_2, F=(15)_{10}=(1111)_2.$
A: This is a lot simpler than converting between base 10 and base 2 or between base 10 and base 16, simply because 16 is a power of 2.  Just convert each base-16 digit to a sequence of four base-2 digits:
$$
\begin{array}{|c|c|}
\text{base 16} & \text{base 2} \\  \hline
1 & 0001 \\
2 & 0010 \\
3 & 0011 \\
4 & 0100 \\
5 & 0101 \\
6 & 0110 \\
7 & 0111 \\
8 & 1000 \\
9 & 1001 \\
A & 1010 \\
B & 1011 \\
C & 1100 \\
D & 1101 \\
E & 1110 \\
F & 1111 \\  \hline
\end{array}
$$
You can drop initial 0s.
Thus $3BF$ becomes 001110111111, and the two initial 0s get dropped.
A: I have been discussing your answers yesterday.
One solution that came out also is to take the Hex values from the right to the left and divide each value by 2 until 0. The rest of the division is written down also from the right to the left. For small numbers, which cant be divided 4 times, the digits are filled with 0. (Not necesary for leading hex digits)
E.g.
3BF
F = 15
15/2 = 7 rest 1
 7/2 = 3 rest 1
 3/2 = 1 rest 1
 1/2 = 0 rest 1

the binary digits for F are: 1111
3BF
B = 11
11/2 = 5 rest 1
 5/2 = 2 rest 1
 2/2 = 1 rest 0
 1/2 = 0 rest 1

the binary digits for B are: 1011
3BF
3/2 = 1 rest 1
1/2 = 0 rest 1
filler       0 (not necesary at the leading hex digit)
filler       0

the binary digits for 3 are 0011
3BF = 1110111111
