In a signed binary in two's complement representation, the first bit (the leftmost) indicates the sign, 1 = negative, 0 = positive.
2. Get the binary representation in one's complement.
* Run this step only if the number is negative *
Note on binary subtraction rules:
11 - 1 = 10; 10 - 1 = 1; 1 - 0 = 1; 1 - 1 = 0.
Subtract 1 from the initial binary number.
* Not the case - the number is positive *
3. 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 *
4. 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
0 241
0 240
0 239
0 238
0 237
0 236
0 235
1 234
0 233
1 232
1 231
0 230
1 229
1 228
1 227
1 226
0 225
1 224
1 223
0 222
0 221
1 220
1 219
1 218
1 217
1 216
0 215
0 214
1 213
1 212
1 211
1 210
0 29
1 28
1 27
0 26
1 25
0 24
1 23
1 22
0 21
1 20
1
5. Multiply each bit by its corresponding power of 2 and add all the terms up.
0000 0000 0000 0000 0000 0000 0000 1011 0111 1011 0011 1110 0111 1011 0101 1011(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 + 0 × 242 + 0 × 241 + 0 × 240 + 0 × 239 + 0 × 238 + 0 × 237 + 0 × 236 + 1 × 235 + 0 × 234 + 1 × 233 + 1 × 232 + 0 × 231 + 1 × 230 + 1 × 229 + 1 × 228 + 1 × 227 + 0 × 226 + 1 × 225 + 1 × 224 + 0 × 223 + 0 × 222 + 1 × 221 + 1 × 220 + 1 × 219 + 1 × 218 + 1 × 217 + 0 × 216 + 0 × 215 + 1 × 214 + 1 × 213 + 1 × 212 + 1 × 211 + 0 × 210 + 1 × 29 + 1 × 28 + 0 × 27 + 1 × 26 + 0 × 25 + 1 × 24 + 1 × 23 + 0 × 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 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 34 359 738 368 + 0 + 8 589 934 592 + 4 294 967 296 + 0 + 1 073 741 824 + 536 870 912 + 268 435 456 + 134 217 728 + 0 + 33 554 432 + 16 777 216 + 0 + 0 + 2 097 152 + 1 048 576 + 524 288 + 262 144 + 131 072 + 0 + 0 + 16 384 + 8 192 + 4 096 + 2 048 + 0 + 512 + 256 + 0 + 64 + 0 + 16 + 8 + 0 + 2 + 1)(10) =
(34 359 738 368 + 8 589 934 592 + 4 294 967 296 + 1 073 741 824 + 536 870 912 + 268 435 456 + 134 217 728 + 33 554 432 + 16 777 216 + 2 097 152 + 1 048 576 + 524 288 + 262 144 + 131 072 + 16 384 + 8 192 + 4 096 + 2 048 + 512 + 256 + 64 + 16 + 8 + 2 + 1)(10) =
49 312 332 635(10)
6. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0000 0000 0000 0000 0000 0000 0000 1011 0111 1011 0011 1110 0111 1011 0101 1011(2) = 49 312 332 635(10)
The signed binary number in two's complement representation 0000 0000 0000 0000 0000 0000 0000 1011 0111 1011 0011 1110 0111 1011 0101 1011(2) converted and written as an integer in decimal system (base ten):
0000 0000 0000 0000 0000 0000 0000 1011 0111 1011 0011 1110 0111 1011 0101 1011(2) = 49 312 332 635(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.