## How to convert signed binary numbers in one's complement representation from binary system to decimal

### To understand how to convert a signed binary number in one's complement representation from binary system to decimal (base ten), the easiest way is to do it through an example - convert binary, 1001 1101, to base ten:

- In a signed binary one's complement, first bit (leftmost) indicates the sign, 1 = negative, 0 = positive. The first bit is 1, so our number is negative.
- Get the binary representation of the positive number, flip all the bits in the signed binary one's complement representation (reversing the digits) - replace the bits set on 1 with 0s and the bits on 0 with 1s:

!(1001 1101) = 0110 0010 - Write bellow the positive binary number representation 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 by increasing each corresonding power of 2 by exactly one unit:
powers of 2: 7 6 5 4 3 2 1 0 digits: 0 1 1 0 0 0 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:
#### 0110 0010

_{(2)}=#### (0 × 2

^{7}+ 1 × 2^{6}+ 1 × 2^{5}+ 0 × 2^{4}+ 0 × 2^{3}+ 0 × 2^{2}+ 1 × 2^{1}+ 0 × 2^{0})_{(10)}=#### (0 + 64 + 32 + 0 + 0 + 0 + 2 + 0)

_{(10)}=#### (64 + 32 + 2)

_{(10)}=#### 98

_{(10)} #### Signed binary number in one's complement representation, 1001 1110 = -98

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