Signed binary two's complement 1011 1111(2) to an integer in decimal system (in base 10) = ?
1. Is this a positive or a negative number?
In a signed binary two's complement, first bit (the leftmost) indicates the sign,
1 = negative, 0 = positive.
1011 1111 is the binary representation of a negative integer, on 8 bits.
2. Get the binary representation in one's complement:
* Run this step only if the number is negative *
Subtract 1 from the binary initial number:
1011 1111 - 1 = 1011 1110
3. Get the binary representation of the positive (unsigned) number:
* Run this step only if the number is negative *
Flip all the bits in the signed binary one's complement representation (reverse the digits) - replace the bits set on 1 with 0s and the bits on 0 with 1s:
!(1011 1110) = 0100 0001
4. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
27
0 26
1 25
0 24
0 23
0 22
0 21
0 20
1
5. Multiply each bit by its corresponding power of 2 and add all the terms up:
0100 0001(2) =
(0 × 27 + 1 × 26 + 0 × 25 + 0 × 24 + 0 × 23 + 0 × 22 + 0 × 21 + 1 × 20)(10) =
(0 + 64 + 0 + 0 + 0 + 0 + 0 + 1)(10) =
(64 + 1)(10) =
65(10)
6. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
1011 1111(2) = -65(10)
Number 1011 1111(2) converted from signed binary two's complement representation to an integer in decimal system (in base 10):
1011 1111(2) = -65(10)
Spaces used to group digits: for binary, by 4.
More operations of this kind:
Convert signed binary two's complement numbers to decimal system (base ten) integers
Entered binary number length must be: 2, 4, 8, 16, 32, or 64 - otherwise extra bits on 0 will be added in front (to the left).