## How to convert signed binary numbers from binary system to decimal (base ten)

### 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 the binary number, 1001 1110, to base ten:

- In a signed binary, the 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 our number is negative.
- Write bellow the binary number in base two, and above each bit that makes up the binary number write the corresponding power of 2 (numeral base) that its place value represents, starting with zero, from the right of the number (rightmost bit), walking to the left of the number and increasing each corresonding power of 2 by 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 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 adding all the terms up, 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})_{(10)}=#### - (0 + 0 + 16 + 8 + 4 + 2 + 0)

_{(10)}=#### - (16 + 8 + 4 + 2)

_{(10)}=#### -30

_{(10)} #### Binary signed number, 1001 1110 = -30

_{(10)}, signed negative integer in base 10