1. Is this a positive or a negative number?
0000 0000 0000 0000 0000 0000 1011 0110 1110 0101 1011 0110 1110 0101 1110 1011 is the binary representation of a positive integer, on 64 bits (8 Bytes).
In a signed binary in two's complement representation, the first bit (the leftmost) indicates the sign, 1 = negative, 0 = positive.
2. Get the binary representation in one's complement.
* Run this step only if the number is negative *
Note on binary subtraction rules:
11 - 1 = 10; 10 - 1 = 1; 1 - 0 = 1; 1 - 1 = 0.
Subtract 1 from the initial binary number.
* Not the case - the number is positive *
3. 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 *
4. 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
1 238
0 237
1 236
1 235
0 234
1 233
1 232
0 231
1 230
1 229
1 228
0 227
0 226
1 225
0 224
1 223
1 222
0 221
1 220
1 219
0 218
1 217
1 216
0 215
1 214
1 213
1 212
0 211
0 210
1 29
0 28
1 27
1 26
1 25
1 24
0 23
1 22
0 21
1 20
1
5. Multiply each bit by its corresponding power of 2 and add all the terms up.
0000 0000 0000 0000 0000 0000 1011 0110 1110 0101 1011 0110 1110 0101 1110 1011(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 + 1 × 239 + 0 × 238 + 1 × 237 + 1 × 236 + 0 × 235 + 1 × 234 + 1 × 233 + 0 × 232 + 1 × 231 + 1 × 230 + 1 × 229 + 0 × 228 + 0 × 227 + 1 × 226 + 0 × 225 + 1 × 224 + 1 × 223 + 0 × 222 + 1 × 221 + 1 × 220 + 0 × 219 + 1 × 218 + 1 × 217 + 0 × 216 + 1 × 215 + 1 × 214 + 1 × 213 + 0 × 212 + 0 × 211 + 1 × 210 + 0 × 29 + 1 × 28 + 1 × 27 + 1 × 26 + 1 × 25 + 0 × 24 + 1 × 23 + 0 × 22 + 1 × 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 + 549 755 813 888 + 0 + 137 438 953 472 + 68 719 476 736 + 0 + 17 179 869 184 + 8 589 934 592 + 0 + 2 147 483 648 + 1 073 741 824 + 536 870 912 + 0 + 0 + 67 108 864 + 0 + 16 777 216 + 8 388 608 + 0 + 2 097 152 + 1 048 576 + 0 + 262 144 + 131 072 + 0 + 32 768 + 16 384 + 8 192 + 0 + 0 + 1 024 + 0 + 256 + 128 + 64 + 32 + 0 + 8 + 0 + 2 + 1)(10) =
(549 755 813 888 + 137 438 953 472 + 68 719 476 736 + 17 179 869 184 + 8 589 934 592 + 2 147 483 648 + 1 073 741 824 + 536 870 912 + 67 108 864 + 16 777 216 + 8 388 608 + 2 097 152 + 1 048 576 + 262 144 + 131 072 + 32 768 + 16 384 + 8 192 + 1 024 + 256 + 128 + 64 + 32 + 8 + 2 + 1)(10) =
785 538 016 747(10)
6. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0000 0000 0000 0000 0000 0000 1011 0110 1110 0101 1011 0110 1110 0101 1110 1011(2) = 785 538 016 747(10)
The signed binary number in two's complement representation 0000 0000 0000 0000 0000 0000 1011 0110 1110 0101 1011 0110 1110 0101 1110 1011(2) converted and written as an integer in decimal system (base ten):
0000 0000 0000 0000 0000 0000 1011 0110 1110 0101 1011 0110 1110 0101 1110 1011(2) = 785 538 016 747(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.