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 0000 0000 0101 0111 1000 0111 0001 0101 0101 0110 0010 1110 0001 = 000 0000 0000 0000 0000 0101 0111 1000 0111 0001 0101 0101 0110 0010 1110 0001
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
0 247
0 246
0 245
0 244
0 243
0 242
1 241
0 240
1 239
0 238
1 237
1 236
1 235
1 234
0 233
0 232
0 231
0 230
1 229
1 228
1 227
0 226
0 225
0 224
1 223
0 222
1 221
0 220
1 219
0 218
1 217
0 216
1 215
0 214
1 213
1 212
0 211
0 210
0 29
1 28
0 27
1 26
1 25
1 24
0 23
0 22
0 21
0 20
1
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
000 0000 0000 0000 0000 0101 0111 1000 0111 0001 0101 0101 0110 0010 1110 0001(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 + 0 × 248 + 0 × 247 + 0 × 246 + 0 × 245 + 0 × 244 + 0 × 243 + 1 × 242 + 0 × 241 + 1 × 240 + 0 × 239 + 1 × 238 + 1 × 237 + 1 × 236 + 1 × 235 + 0 × 234 + 0 × 233 + 0 × 232 + 0 × 231 + 1 × 230 + 1 × 229 + 1 × 228 + 0 × 227 + 0 × 226 + 0 × 225 + 1 × 224 + 0 × 223 + 1 × 222 + 0 × 221 + 1 × 220 + 0 × 219 + 1 × 218 + 0 × 217 + 1 × 216 + 0 × 215 + 1 × 214 + 1 × 213 + 0 × 212 + 0 × 211 + 0 × 210 + 1 × 29 + 0 × 28 + 1 × 27 + 1 × 26 + 1 × 25 + 0 × 24 + 0 × 23 + 0 × 22 + 0 × 21 + 1 × 20)(10) =
(0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 4 398 046 511 104 + 0 + 1 099 511 627 776 + 0 + 274 877 906 944 + 137 438 953 472 + 68 719 476 736 + 34 359 738 368 + 0 + 0 + 0 + 0 + 1 073 741 824 + 536 870 912 + 268 435 456 + 0 + 0 + 0 + 16 777 216 + 0 + 4 194 304 + 0 + 1 048 576 + 0 + 262 144 + 0 + 65 536 + 0 + 16 384 + 8 192 + 0 + 0 + 0 + 512 + 0 + 128 + 64 + 32 + 0 + 0 + 0 + 0 + 1)(10) =
(4 398 046 511 104 + 1 099 511 627 776 + 274 877 906 944 + 137 438 953 472 + 68 719 476 736 + 34 359 738 368 + 1 073 741 824 + 536 870 912 + 268 435 456 + 16 777 216 + 4 194 304 + 1 048 576 + 262 144 + 65 536 + 16 384 + 8 192 + 512 + 128 + 64 + 32 + 1)(10) =
6 014 855 635 681(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0000 0000 0000 0000 0000 0101 0111 1000 0111 0001 0101 0101 0110 0010 1110 0001(2) = 6 014 855 635 681(10)
The number 0000 0000 0000 0000 0000 0101 0111 1000 0111 0001 0101 0101 0110 0010 1110 0001(2) converted from a signed binary (base two) and written as an integer in decimal system (base ten):
0000 0000 0000 0000 0000 0101 0111 1000 0111 0001 0101 0101 0110 0010 1110 0001(2) = 6 014 855 635 681(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.