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:
263
0 262
0 261
0 260
0 259
0 258
0 257
0 256
0 255
0 254
0 253
0 252
0 251
0 250
0 249
0 248
0 247
0 246
0 245
0 244
0 243
0 242
1 241
0 240
0 239
0 238
0 237
1 236
0 235
0 234
1 233
0 232
0 231
0 230
0 229
1 228
0 227
0 226
0 225
1 224
1 223
1 222
0 221
0 220
0 219
0 218
0 217
1 216
0 215
0 214
0 213
0 212
0 211
0 210
1 29
0 28
0 27
0 26
0 25
1 24
0 23
0 22
1 21
1 20
1
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
0000 0000 0000 0000 0000 0100 0010 0100 0010 0011 1000 0010 0000 0100 0010 0111(2) =
(0 × 263 + 0 × 262 + 0 × 261 + 0 × 260 + 0 × 259 + 0 × 258 + 0 × 257 + 0 × 256 + 0 × 255 + 0 × 254 + 0 × 253 + 0 × 252 + 0 × 251 + 0 × 250 + 0 × 249 + 0 × 248 + 0 × 247 + 0 × 246 + 0 × 245 + 0 × 244 + 0 × 243 + 1 × 242 + 0 × 241 + 0 × 240 + 0 × 239 + 0 × 238 + 1 × 237 + 0 × 236 + 0 × 235 + 1 × 234 + 0 × 233 + 0 × 232 + 0 × 231 + 0 × 230 + 1 × 229 + 0 × 228 + 0 × 227 + 0 × 226 + 1 × 225 + 1 × 224 + 1 × 223 + 0 × 222 + 0 × 221 + 0 × 220 + 0 × 219 + 0 × 218 + 1 × 217 + 0 × 216 + 0 × 215 + 0 × 214 + 0 × 213 + 0 × 212 + 0 × 211 + 1 × 210 + 0 × 29 + 0 × 28 + 0 × 27 + 0 × 26 + 1 × 25 + 0 × 24 + 0 × 23 + 1 × 22 + 1 × 21 + 1 × 20)(10) =
(0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 4 398 046 511 104 + 0 + 0 + 0 + 0 + 137 438 953 472 + 0 + 0 + 17 179 869 184 + 0 + 0 + 0 + 0 + 536 870 912 + 0 + 0 + 0 + 33 554 432 + 16 777 216 + 8 388 608 + 0 + 0 + 0 + 0 + 0 + 131 072 + 0 + 0 + 0 + 0 + 0 + 0 + 1 024 + 0 + 0 + 0 + 0 + 32 + 0 + 0 + 4 + 2 + 1)(10) =
(4 398 046 511 104 + 137 438 953 472 + 17 179 869 184 + 536 870 912 + 33 554 432 + 16 777 216 + 8 388 608 + 131 072 + 1 024 + 32 + 4 + 2 + 1)(10) =
4 553 261 057 063(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0000 0000 0000 0000 0000 0100 0010 0100 0010 0011 1000 0010 0000 0100 0010 0111(2) = 4 553 261 057 063(10)
The signed binary number in one's complement representation 0000 0000 0000 0000 0000 0100 0010 0100 0010 0011 1000 0010 0000 0100 0010 0111(2) converted and written as an integer in decimal system (base ten):
0000 0000 0000 0000 0000 0100 0010 0100 0010 0011 1000 0010 0000 0100 0010 0111(2) = 4 553 261 057 063(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.