In a signed binary, the first bit (the leftmost) is reserved for the sign,
1 = negative, 0 = positive. This bit does not count when calculating the absolute value.
2. Construct the unsigned binary number.
Exclude the first bit (the leftmost), that is reserved for the sign:
0000 1000 1111 1101 = 000 1000 1111 1101
3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
214
0 213
0 212
0 211
1 210
0 29
0 28
0 27
1 26
1 25
1 24
1 23
1 22
1 21
0 20
1
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
000 1000 1111 1101(2) =
(0 × 214 + 0 × 213 + 0 × 212 + 1 × 211 + 0 × 210 + 0 × 29 + 0 × 28 + 1 × 27 + 1 × 26 + 1 × 25 + 1 × 24 + 1 × 23 + 1 × 22 + 0 × 21 + 1 × 20)(10) =
(0 + 0 + 0 + 2 048 + 0 + 0 + 0 + 128 + 64 + 32 + 16 + 8 + 4 + 0 + 1)(10) =
(2 048 + 128 + 64 + 32 + 16 + 8 + 4 + 1)(10) =
2 301(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0000 1000 1111 1101(2) = 2 301(10)
The number 0000 1000 1111 1101(2) converted from a signed binary (base two) and written as an integer in decimal system (base ten):
0000 1000 1111 1101(2) = 2 301(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.