In a signed binary in one's complement representation, the first bit (the leftmost) indicates the sign, 1 = negative, 0 = positive.
2. Get the binary representation of the positive (unsigned) number.
* Run this step only if the number is negative *
Flip all the bits of the signed binary in one's complement representation (reverse the digits) - replace the bits set on 1 with 0s and the bits on 0 with 1s:
* Not the case - the number is positive *
3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
231
0 230
1 229
0 228
0 227
0 226
0 225
0 224
1 223
0 222
1 221
0 220
0 219
0 218
1 217
0 216
1 215
0 214
1 213
0 212
0 211
1 210
1 29
0 28
1 27
0 26
1 25
0 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.
0100 0001 0100 0101 0100 1101 0101 1101(2) =
(0 × 231 + 1 × 230 + 0 × 229 + 0 × 228 + 0 × 227 + 0 × 226 + 0 × 225 + 1 × 224 + 0 × 223 + 1 × 222 + 0 × 221 + 0 × 220 + 0 × 219 + 1 × 218 + 0 × 217 + 1 × 216 + 0 × 215 + 1 × 214 + 0 × 213 + 0 × 212 + 1 × 211 + 1 × 210 + 0 × 29 + 1 × 28 + 0 × 27 + 1 × 26 + 0 × 25 + 1 × 24 + 1 × 23 + 1 × 22 + 0 × 21 + 1 × 20)(10) =
(0 + 1 073 741 824 + 0 + 0 + 0 + 0 + 0 + 16 777 216 + 0 + 4 194 304 + 0 + 0 + 0 + 262 144 + 0 + 65 536 + 0 + 16 384 + 0 + 0 + 2 048 + 1 024 + 0 + 256 + 0 + 64 + 0 + 16 + 8 + 4 + 0 + 1)(10) =
(1 073 741 824 + 16 777 216 + 4 194 304 + 262 144 + 65 536 + 16 384 + 2 048 + 1 024 + 256 + 64 + 16 + 8 + 4 + 1)(10) =
1 095 060 829(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0100 0001 0100 0101 0100 1101 0101 1101(2) = 1 095 060 829(10)
The signed binary number in one's complement representation 0100 0001 0100 0101 0100 1101 0101 1101(2) converted and written as an integer in decimal system (base ten):
0100 0001 0100 0101 0100 1101 0101 1101(2) = 1 095 060 829(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.