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:
1011 1110 1000 1101 0011 0111 0000 1011 0110 1011 1011 1100 0110 0010 0000 1101 = 011 1110 1000 1101 0011 0111 0000 1011 0110 1011 1011 1100 0110 0010 0000 1101
3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
262
0 261
1 260
1 259
1 258
1 257
1 256
0 255
1 254
0 253
0 252
0 251
1 250
1 249
0 248
1 247
0 246
0 245
1 244
1 243
0 242
1 241
1 240
1 239
0 238
0 237
0 236
0 235
1 234
0 233
1 232
1 231
0 230
1 229
1 228
0 227
1 226
0 225
1 224
1 223
1 222
0 221
1 220
1 219
1 218
1 217
0 216
0 215
0 214
1 213
1 212
0 211
0 210
0 29
1 28
0 27
0 26
0 25
0 24
0 23
1 22
1 21
0 20
1
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
011 1110 1000 1101 0011 0111 0000 1011 0110 1011 1011 1100 0110 0010 0000 1101(2) =
(0 × 262 + 1 × 261 + 1 × 260 + 1 × 259 + 1 × 258 + 1 × 257 + 0 × 256 + 1 × 255 + 0 × 254 + 0 × 253 + 0 × 252 + 1 × 251 + 1 × 250 + 0 × 249 + 1 × 248 + 0 × 247 + 0 × 246 + 1 × 245 + 1 × 244 + 0 × 243 + 1 × 242 + 1 × 241 + 1 × 240 + 0 × 239 + 0 × 238 + 0 × 237 + 0 × 236 + 1 × 235 + 0 × 234 + 1 × 233 + 1 × 232 + 0 × 231 + 1 × 230 + 1 × 229 + 0 × 228 + 1 × 227 + 0 × 226 + 1 × 225 + 1 × 224 + 1 × 223 + 0 × 222 + 1 × 221 + 1 × 220 + 1 × 219 + 1 × 218 + 0 × 217 + 0 × 216 + 0 × 215 + 1 × 214 + 1 × 213 + 0 × 212 + 0 × 211 + 0 × 210 + 1 × 29 + 0 × 28 + 0 × 27 + 0 × 26 + 0 × 25 + 0 × 24 + 1 × 23 + 1 × 22 + 0 × 21 + 1 × 20)(10) =
(0 + 2 305 843 009 213 693 952 + 1 152 921 504 606 846 976 + 576 460 752 303 423 488 + 288 230 376 151 711 744 + 144 115 188 075 855 872 + 0 + 36 028 797 018 963 968 + 0 + 0 + 0 + 2 251 799 813 685 248 + 1 125 899 906 842 624 + 0 + 281 474 976 710 656 + 0 + 0 + 35 184 372 088 832 + 17 592 186 044 416 + 0 + 4 398 046 511 104 + 2 199 023 255 552 + 1 099 511 627 776 + 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 + 0 + 134 217 728 + 0 + 33 554 432 + 16 777 216 + 8 388 608 + 0 + 2 097 152 + 1 048 576 + 524 288 + 262 144 + 0 + 0 + 0 + 16 384 + 8 192 + 0 + 0 + 0 + 512 + 0 + 0 + 0 + 0 + 0 + 8 + 4 + 0 + 1)(10) =
(2 305 843 009 213 693 952 + 1 152 921 504 606 846 976 + 576 460 752 303 423 488 + 288 230 376 151 711 744 + 144 115 188 075 855 872 + 36 028 797 018 963 968 + 2 251 799 813 685 248 + 1 125 899 906 842 624 + 281 474 976 710 656 + 35 184 372 088 832 + 17 592 186 044 416 + 4 398 046 511 104 + 2 199 023 255 552 + 1 099 511 627 776 + 34 359 738 368 + 8 589 934 592 + 4 294 967 296 + 1 073 741 824 + 536 870 912 + 134 217 728 + 33 554 432 + 16 777 216 + 8 388 608 + 2 097 152 + 1 048 576 + 524 288 + 262 144 + 16 384 + 8 192 + 512 + 8 + 4 + 1)(10) =
4 507 319 324 259 410 445(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
1011 1110 1000 1101 0011 0111 0000 1011 0110 1011 1011 1100 0110 0010 0000 1101(2) = -4 507 319 324 259 410 445(10)
The number 1011 1110 1000 1101 0011 0111 0000 1011 0110 1011 1011 1100 0110 0010 0000 1101(2) converted from a signed binary (base two) and written as an integer in decimal system (base ten):
1011 1110 1000 1101 0011 0111 0000 1011 0110 1011 1011 1100 0110 0010 0000 1101(2) = -4 507 319 324 259 410 445(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.