## How to convert signed binary numbers from binary system to decimal

### To understand how to convert a signed binary number from binary system to decimal (base ten), the easiest way is to do it through an example - convert binary, 1001 1110, to base ten:

- In a signed binary, first bit (leftmost) is reserved for the sign, 1 = negative, 0 = positive. This bit does not count when calculating the absolute value (value without sign). The first bit is 1, so the number is negative.
- Write bellow the binary number in base two, and above each bit that makes up the binary number write the corresponding powers of 2 (numeral base), starting with zero, from the right of the number (rightmost bit), walking to the left of the number, increasing each corresonding power of 2 with exactly one unit, but ignoring the very first bit (the leftmost, the one representing the sign):
powers of 2 6 5 4 3 2 1 0 number's digits 1 0 0 1 1 1 1 0 - Build the representation of the positive number in base 10, by taking each digit of the binary number, multiplying it by the corresponding power of 2 and then summing up all the terms, but also taking care of the number sign:

1001 1110 =

= - (0 * 2^{6}+ 0 * 2^{5}+ 1 * 2^{4}+ 1 * 2^{3}+ 1 * 2^{2}+ 1 * 2^{1}+ 0 * 2^{0}) =

= - (0 + 0 + 16 + 8 + 4 + 2 + 0) =

= - (16 + 8 + 4 + 2) =

= -30_{(10)}