1. Is this a positive or a negative number?
0000 0000 0000 0000 0000 0000 0000 1011 0001 0100 1110 1010 0011 1010 1001 0100 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
0 237
0 236
0 235
1 234
0 233
1 232
1 231
0 230
0 229
0 228
1 227
0 226
1 225
0 224
0 223
1 222
1 221
1 220
0 219
1 218
0 217
1 216
0 215
0 214
0 213
1 212
1 211
1 210
0 29
1 28
0 27
1 26
0 25
0 24
1 23
0 22
1 21
0 20
0
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
0000 0000 0000 0000 0000 0000 0000 1011 0001 0100 1110 1010 0011 1010 1001 0100(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 + 0 × 238 + 0 × 237 + 0 × 236 + 1 × 235 + 0 × 234 + 1 × 233 + 1 × 232 + 0 × 231 + 0 × 230 + 0 × 229 + 1 × 228 + 0 × 227 + 1 × 226 + 0 × 225 + 0 × 224 + 1 × 223 + 1 × 222 + 1 × 221 + 0 × 220 + 1 × 219 + 0 × 218 + 1 × 217 + 0 × 216 + 0 × 215 + 0 × 214 + 1 × 213 + 1 × 212 + 1 × 211 + 0 × 210 + 1 × 29 + 0 × 28 + 1 × 27 + 0 × 26 + 0 × 25 + 1 × 24 + 0 × 23 + 1 × 22 + 0 × 21 + 0 × 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 + 0 + 0 + 0 + 34 359 738 368 + 0 + 8 589 934 592 + 4 294 967 296 + 0 + 0 + 0 + 268 435 456 + 0 + 67 108 864 + 0 + 0 + 8 388 608 + 4 194 304 + 2 097 152 + 0 + 524 288 + 0 + 131 072 + 0 + 0 + 0 + 8 192 + 4 096 + 2 048 + 0 + 512 + 0 + 128 + 0 + 0 + 16 + 0 + 4 + 0 + 0)(10) =
(34 359 738 368 + 8 589 934 592 + 4 294 967 296 + 268 435 456 + 67 108 864 + 8 388 608 + 4 194 304 + 2 097 152 + 524 288 + 131 072 + 8 192 + 4 096 + 2 048 + 512 + 128 + 16 + 4)(10) =
47 595 534 996(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 0000 1011 0001 0100 1110 1010 0011 1010 1001 0100(2) = 47 595 534 996(10)
The signed binary number in one's complement representation 0000 0000 0000 0000 0000 0000 0000 1011 0001 0100 1110 1010 0011 1010 1001 0100(2) converted and written as an integer in decimal system (base ten):
0000 0000 0000 0000 0000 0000 0000 1011 0001 0100 1110 1010 0011 1010 1001 0100(2) = 47 595 534 996(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.