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 0000 0000 0001 0000 1001 1010 1101 1000 0001 0100 1000 0010 1111 1001 1000 = 000 0000 0000 0001 0000 1001 1010 1101 1000 0001 0100 1000 0010 1111 1001 1000
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
0 257
0 256
0 255
0 254
0 253
0 252
0 251
0 250
0 249
0 248
1 247
0 246
0 245
0 244
0 243
1 242
0 241
0 240
1 239
1 238
0 237
1 236
0 235
1 234
1 233
0 232
1 231
1 230
0 229
0 228
0 227
0 226
0 225
0 224
1 223
0 222
1 221
0 220
0 219
1 218
0 217
0 216
0 215
0 214
0 213
1 212
0 211
1 210
1 29
1 28
1 27
1 26
0 25
0 24
1 23
1 22
0 21
0 20
0
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
000 0000 0000 0001 0000 1001 1010 1101 1000 0001 0100 1000 0010 1111 1001 1000(2) =
(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 + 1 × 248 + 0 × 247 + 0 × 246 + 0 × 245 + 0 × 244 + 1 × 243 + 0 × 242 + 0 × 241 + 1 × 240 + 1 × 239 + 0 × 238 + 1 × 237 + 0 × 236 + 1 × 235 + 1 × 234 + 0 × 233 + 1 × 232 + 1 × 231 + 0 × 230 + 0 × 229 + 0 × 228 + 0 × 227 + 0 × 226 + 0 × 225 + 1 × 224 + 0 × 223 + 1 × 222 + 0 × 221 + 0 × 220 + 1 × 219 + 0 × 218 + 0 × 217 + 0 × 216 + 0 × 215 + 0 × 214 + 1 × 213 + 0 × 212 + 1 × 211 + 1 × 210 + 1 × 29 + 1 × 28 + 1 × 27 + 0 × 26 + 0 × 25 + 1 × 24 + 1 × 23 + 0 × 22 + 0 × 21 + 0 × 20)(10) =
(0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 281 474 976 710 656 + 0 + 0 + 0 + 0 + 8 796 093 022 208 + 0 + 0 + 1 099 511 627 776 + 549 755 813 888 + 0 + 137 438 953 472 + 0 + 34 359 738 368 + 17 179 869 184 + 0 + 4 294 967 296 + 2 147 483 648 + 0 + 0 + 0 + 0 + 0 + 0 + 16 777 216 + 0 + 4 194 304 + 0 + 0 + 524 288 + 0 + 0 + 0 + 0 + 0 + 8 192 + 0 + 2 048 + 1 024 + 512 + 256 + 128 + 0 + 0 + 16 + 8 + 0 + 0 + 0)(10) =
(281 474 976 710 656 + 8 796 093 022 208 + 1 099 511 627 776 + 549 755 813 888 + 137 438 953 472 + 34 359 738 368 + 17 179 869 184 + 4 294 967 296 + 2 147 483 648 + 16 777 216 + 4 194 304 + 524 288 + 8 192 + 2 048 + 1 024 + 512 + 256 + 128 + 16 + 8)(10) =
292 115 779 694 488(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0000 0000 0000 0001 0000 1001 1010 1101 1000 0001 0100 1000 0010 1111 1001 1000(2) = 292 115 779 694 488(10)
The number 0000 0000 0000 0001 0000 1001 1010 1101 1000 0001 0100 1000 0010 1111 1001 1000(2) converted from a signed binary (base two) and written as an integer in decimal system (base ten):
0000 0000 0000 0001 0000 1001 1010 1101 1000 0001 0100 1000 0010 1111 1001 1000(2) = 292 115 779 694 488(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.