1. Is this a positive or a negative number?
0000 0000 0000 0000 0000 0000 0110 1001 1100 1010 1001 0110 1010 1000 1010 0001 is the binary representation of a positive integer, on 64 bits (8 Bytes).
In a signed binary in one's complement representation, the first bit (the leftmost) indicates the sign, 1 = negative, 0 = positive.
2. 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 *
3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
263
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
0 242
0 241
0 240
0 239
0 238
1 237
1 236
0 235
1 234
0 233
0 232
1 231
1 230
1 229
0 228
0 227
1 226
0 225
1 224
0 223
1 222
0 221
0 220
1 219
0 218
1 217
1 216
0 215
1 214
0 213
1 212
0 211
1 210
0 29
0 28
0 27
1 26
0 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.
0000 0000 0000 0000 0000 0000 0110 1001 1100 1010 1001 0110 1010 1000 1010 0001(2) =
(0 × 263 + 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 + 0 × 242 + 0 × 241 + 0 × 240 + 0 × 239 + 1 × 238 + 1 × 237 + 0 × 236 + 1 × 235 + 0 × 234 + 0 × 233 + 1 × 232 + 1 × 231 + 1 × 230 + 0 × 229 + 0 × 228 + 1 × 227 + 0 × 226 + 1 × 225 + 0 × 224 + 1 × 223 + 0 × 222 + 0 × 221 + 1 × 220 + 0 × 219 + 1 × 218 + 1 × 217 + 0 × 216 + 1 × 215 + 0 × 214 + 1 × 213 + 0 × 212 + 1 × 211 + 0 × 210 + 0 × 29 + 0 × 28 + 1 × 27 + 0 × 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 + 0 + 0 + 0 + 0 + 0 + 274 877 906 944 + 137 438 953 472 + 0 + 34 359 738 368 + 0 + 0 + 4 294 967 296 + 2 147 483 648 + 1 073 741 824 + 0 + 0 + 134 217 728 + 0 + 33 554 432 + 0 + 8 388 608 + 0 + 0 + 1 048 576 + 0 + 262 144 + 131 072 + 0 + 32 768 + 0 + 8 192 + 0 + 2 048 + 0 + 0 + 0 + 128 + 0 + 32 + 0 + 0 + 0 + 0 + 1)(10) =
(274 877 906 944 + 137 438 953 472 + 34 359 738 368 + 4 294 967 296 + 2 147 483 648 + 1 073 741 824 + 134 217 728 + 33 554 432 + 8 388 608 + 1 048 576 + 262 144 + 131 072 + 32 768 + 8 192 + 2 048 + 128 + 32 + 1)(10) =
454 370 437 281(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 0000 0110 1001 1100 1010 1001 0110 1010 1000 1010 0001(2) = 454 370 437 281(10)
The signed binary number in one's complement representation 0000 0000 0000 0000 0000 0000 0110 1001 1100 1010 1001 0110 1010 1000 1010 0001(2) converted and written as an integer in decimal system (base ten):
0000 0000 0000 0000 0000 0000 0110 1001 1100 1010 1001 0110 1010 1000 1010 0001(2) = 454 370 437 281(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.