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
1 261
0 260
0 259
0 258
1 257
1 256
1 255
1 254
1 253
0 252
0 251
0 250
0 249
1 248
0 247
0 246
0 245
0 244
0 243
1 242
0 241
1 240
1 239
0 238
0 237
0 236
0 235
1 234
1 233
1 232
1 231
0 230
0 229
0 228
0 227
0 226
0 225
0 224
0 223
0 222
0 221
0 220
0 219
0 218
0 217
0 216
0 215
0 214
0 213
0 212
0 211
0 210
0 29
0 28
0 27
0 26
0 25
0 24
0 23
0 22
0 21
0 20
0
5. Multiply each bit by its corresponding power of 2 and add all the terms up.
0100 0111 1100 0010 0000 1011 0000 1111 0000 0000 0000 0000 0000 0000 0000 0000(2) =
(0 × 263 + 1 × 262 + 0 × 261 + 0 × 260 + 0 × 259 + 1 × 258 + 1 × 257 + 1 × 256 + 1 × 255 + 1 × 254 + 0 × 253 + 0 × 252 + 0 × 251 + 0 × 250 + 1 × 249 + 0 × 248 + 0 × 247 + 0 × 246 + 0 × 245 + 0 × 244 + 1 × 243 + 0 × 242 + 1 × 241 + 1 × 240 + 0 × 239 + 0 × 238 + 0 × 237 + 0 × 236 + 1 × 235 + 1 × 234 + 1 × 233 + 1 × 232 + 0 × 231 + 0 × 230 + 0 × 229 + 0 × 228 + 0 × 227 + 0 × 226 + 0 × 225 + 0 × 224 + 0 × 223 + 0 × 222 + 0 × 221 + 0 × 220 + 0 × 219 + 0 × 218 + 0 × 217 + 0 × 216 + 0 × 215 + 0 × 214 + 0 × 213 + 0 × 212 + 0 × 211 + 0 × 210 + 0 × 29 + 0 × 28 + 0 × 27 + 0 × 26 + 0 × 25 + 0 × 24 + 0 × 23 + 0 × 22 + 0 × 21 + 0 × 20)(10) =
(0 + 4 611 686 018 427 387 904 + 0 + 0 + 0 + 288 230 376 151 711 744 + 144 115 188 075 855 872 + 72 057 594 037 927 936 + 36 028 797 018 963 968 + 18 014 398 509 481 984 + 0 + 0 + 0 + 0 + 562 949 953 421 312 + 0 + 0 + 0 + 0 + 0 + 8 796 093 022 208 + 0 + 2 199 023 255 552 + 1 099 511 627 776 + 0 + 0 + 0 + 0 + 34 359 738 368 + 17 179 869 184 + 8 589 934 592 + 4 294 967 296 + 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 + 0 + 0 + 0 + 0)(10) =
(4 611 686 018 427 387 904 + 288 230 376 151 711 744 + 144 115 188 075 855 872 + 72 057 594 037 927 936 + 36 028 797 018 963 968 + 18 014 398 509 481 984 + 562 949 953 421 312 + 8 796 093 022 208 + 2 199 023 255 552 + 1 099 511 627 776 + 34 359 738 368 + 17 179 869 184 + 8 589 934 592 + 4 294 967 296)(10) =
5 170 707 481 227 165 696(10)
6. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0100 0111 1100 0010 0000 1011 0000 1111 0000 0000 0000 0000 0000 0000 0000 0000(2) = 5 170 707 481 227 165 696(10)
The signed binary number in two's complement representation 0100 0111 1100 0010 0000 1011 0000 1111 0000 0000 0000 0000 0000 0000 0000 0000(2) converted and written as an integer in decimal system (base ten):
0100 0111 1100 0010 0000 1011 0000 1111 0000 0000 0000 0000 0000 0000 0000 0000(2) = 5 170 707 481 227 165 696(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.