How to convert a signed binary:
1111 0111 1111 1111(2)
to an integer in decimal system (in base 10)
1. Is this a positive or a negative number?
In a signed binary, first bit (the leftmost) is reserved for the sign, 1 = negative, 0 = positive. This bit does not count when calculating the absolute value.
1111 0111 1111 1111 is the binary representation of a negative integer, on 16 bits (2 Bytes).
2. Construct the unsigned binary number, exclude the first bit (the leftmost), that is reserved for the sign:
1111 0111 1111 1111 = 111 0111 1111 1111
3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
214
1 213
1 212
1 211
0 210
1 29
1 28
1 27
1 26
1 25
1 24
1 23
1 22
1 21
1 20
1
4. Multiply each bit by its corresponding power of 2 and add all the terms up:
111 0111 1111 1111(2) =
(1 × 214 + 1 × 213 + 1 × 212 + 0 × 211 + 1 × 210 + 1 × 29 + 1 × 28 + 1 × 27 + 1 × 26 + 1 × 25 + 1 × 24 + 1 × 23 + 1 × 22 + 1 × 21 + 1 × 20)(10) =
(16 384 + 8 192 + 4 096 + 0 + 1 024 + 512 + 256 + 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1)(10) =
(16 384 + 8 192 + 4 096 + 1 024 + 512 + 256 + 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1)(10) =
30 719(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
1111 0111 1111 1111(2) = -30 719(10)
Conclusion: