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:
0000 0111 0011 0001 1000 0000 1111 1011 1101 0000 1000 0111 0000 1111 1011 1111 = 000 0111 0011 0001 1000 0000 1111 1011 1101 0000 1000 0111 0000 1111 1011 1111
3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
262
0 261
0 260
0 259
0 258
1 257
1 256
1 255
0 254
0 253
1 252
1 251
0 250
0 249
0 248
1 247
1 246
0 245
0 244
0 243
0 242
0 241
0 240
0 239
1 238
1 237
1 236
1 235
1 234
0 233
1 232
1 231
1 230
1 229
0 228
1 227
0 226
0 225
0 224
0 223
1 222
0 221
0 220
0 219
0 218
1 217
1 216
1 215
0 214
0 213
0 212
0 211
1 210
1 29
1 28
1 27
1 26
0 25
1 24
1 23
1 22
1 21
1 20
1
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
000 0111 0011 0001 1000 0000 1111 1011 1101 0000 1000 0111 0000 1111 1011 1111(2) =
(0 × 262 + 0 × 261 + 0 × 260 + 0 × 259 + 1 × 258 + 1 × 257 + 1 × 256 + 0 × 255 + 0 × 254 + 1 × 253 + 1 × 252 + 0 × 251 + 0 × 250 + 0 × 249 + 1 × 248 + 1 × 247 + 0 × 246 + 0 × 245 + 0 × 244 + 0 × 243 + 0 × 242 + 0 × 241 + 0 × 240 + 1 × 239 + 1 × 238 + 1 × 237 + 1 × 236 + 1 × 235 + 0 × 234 + 1 × 233 + 1 × 232 + 1 × 231 + 1 × 230 + 0 × 229 + 1 × 228 + 0 × 227 + 0 × 226 + 0 × 225 + 0 × 224 + 1 × 223 + 0 × 222 + 0 × 221 + 0 × 220 + 0 × 219 + 1 × 218 + 1 × 217 + 1 × 216 + 0 × 215 + 0 × 214 + 0 × 213 + 0 × 212 + 1 × 211 + 1 × 210 + 1 × 29 + 1 × 28 + 1 × 27 + 0 × 26 + 1 × 25 + 1 × 24 + 1 × 23 + 1 × 22 + 1 × 21 + 1 × 20)(10) =
(0 + 0 + 0 + 0 + 288 230 376 151 711 744 + 144 115 188 075 855 872 + 72 057 594 037 927 936 + 0 + 0 + 9 007 199 254 740 992 + 4 503 599 627 370 496 + 0 + 0 + 0 + 281 474 976 710 656 + 140 737 488 355 328 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 549 755 813 888 + 274 877 906 944 + 137 438 953 472 + 68 719 476 736 + 34 359 738 368 + 0 + 8 589 934 592 + 4 294 967 296 + 2 147 483 648 + 1 073 741 824 + 0 + 268 435 456 + 0 + 0 + 0 + 0 + 8 388 608 + 0 + 0 + 0 + 0 + 262 144 + 131 072 + 65 536 + 0 + 0 + 0 + 0 + 2 048 + 1 024 + 512 + 256 + 128 + 0 + 32 + 16 + 8 + 4 + 2 + 1)(10) =
(288 230 376 151 711 744 + 144 115 188 075 855 872 + 72 057 594 037 927 936 + 9 007 199 254 740 992 + 4 503 599 627 370 496 + 281 474 976 710 656 + 140 737 488 355 328 + 549 755 813 888 + 274 877 906 944 + 137 438 953 472 + 68 719 476 736 + 34 359 738 368 + 8 589 934 592 + 4 294 967 296 + 2 147 483 648 + 1 073 741 824 + 268 435 456 + 8 388 608 + 262 144 + 131 072 + 65 536 + 2 048 + 1 024 + 512 + 256 + 128 + 32 + 16 + 8 + 4 + 2 + 1)(10) =
518 337 251 147 976 639(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0000 0111 0011 0001 1000 0000 1111 1011 1101 0000 1000 0111 0000 1111 1011 1111(2) = 518 337 251 147 976 639(10)
The number 0000 0111 0011 0001 1000 0000 1111 1011 1101 0000 1000 0111 0000 1111 1011 1111(2) converted from a signed binary (base two) and written as an integer in decimal system (base ten):
0000 0111 0011 0001 1000 0000 1111 1011 1101 0000 1000 0111 0000 1111 1011 1111(2) = 518 337 251 147 976 639(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.