1. Divide the number repeatedly by 2:
Keep track of each remainder.
We stop when we get a quotient that is equal to zero.
- division = quotient + remainder;
- 4 884 848 484 848 486 ÷ 2 = 2 442 424 242 424 243 + 0;
- 2 442 424 242 424 243 ÷ 2 = 1 221 212 121 212 121 + 1;
- 1 221 212 121 212 121 ÷ 2 = 610 606 060 606 060 + 1;
- 610 606 060 606 060 ÷ 2 = 305 303 030 303 030 + 0;
- 305 303 030 303 030 ÷ 2 = 152 651 515 151 515 + 0;
- 152 651 515 151 515 ÷ 2 = 76 325 757 575 757 + 1;
- 76 325 757 575 757 ÷ 2 = 38 162 878 787 878 + 1;
- 38 162 878 787 878 ÷ 2 = 19 081 439 393 939 + 0;
- 19 081 439 393 939 ÷ 2 = 9 540 719 696 969 + 1;
- 9 540 719 696 969 ÷ 2 = 4 770 359 848 484 + 1;
- 4 770 359 848 484 ÷ 2 = 2 385 179 924 242 + 0;
- 2 385 179 924 242 ÷ 2 = 1 192 589 962 121 + 0;
- 1 192 589 962 121 ÷ 2 = 596 294 981 060 + 1;
- 596 294 981 060 ÷ 2 = 298 147 490 530 + 0;
- 298 147 490 530 ÷ 2 = 149 073 745 265 + 0;
- 149 073 745 265 ÷ 2 = 74 536 872 632 + 1;
- 74 536 872 632 ÷ 2 = 37 268 436 316 + 0;
- 37 268 436 316 ÷ 2 = 18 634 218 158 + 0;
- 18 634 218 158 ÷ 2 = 9 317 109 079 + 0;
- 9 317 109 079 ÷ 2 = 4 658 554 539 + 1;
- 4 658 554 539 ÷ 2 = 2 329 277 269 + 1;
- 2 329 277 269 ÷ 2 = 1 164 638 634 + 1;
- 1 164 638 634 ÷ 2 = 582 319 317 + 0;
- 582 319 317 ÷ 2 = 291 159 658 + 1;
- 291 159 658 ÷ 2 = 145 579 829 + 0;
- 145 579 829 ÷ 2 = 72 789 914 + 1;
- 72 789 914 ÷ 2 = 36 394 957 + 0;
- 36 394 957 ÷ 2 = 18 197 478 + 1;
- 18 197 478 ÷ 2 = 9 098 739 + 0;
- 9 098 739 ÷ 2 = 4 549 369 + 1;
- 4 549 369 ÷ 2 = 2 274 684 + 1;
- 2 274 684 ÷ 2 = 1 137 342 + 0;
- 1 137 342 ÷ 2 = 568 671 + 0;
- 568 671 ÷ 2 = 284 335 + 1;
- 284 335 ÷ 2 = 142 167 + 1;
- 142 167 ÷ 2 = 71 083 + 1;
- 71 083 ÷ 2 = 35 541 + 1;
- 35 541 ÷ 2 = 17 770 + 1;
- 17 770 ÷ 2 = 8 885 + 0;
- 8 885 ÷ 2 = 4 442 + 1;
- 4 442 ÷ 2 = 2 221 + 0;
- 2 221 ÷ 2 = 1 110 + 1;
- 1 110 ÷ 2 = 555 + 0;
- 555 ÷ 2 = 277 + 1;
- 277 ÷ 2 = 138 + 1;
- 138 ÷ 2 = 69 + 0;
- 69 ÷ 2 = 34 + 1;
- 34 ÷ 2 = 17 + 0;
- 17 ÷ 2 = 8 + 1;
- 8 ÷ 2 = 4 + 0;
- 4 ÷ 2 = 2 + 0;
- 2 ÷ 2 = 1 + 0;
- 1 ÷ 2 = 0 + 1;
2. Construct the base 2 representation of the positive number:
Take all the remainders starting from the bottom of the list constructed above.
4 884 848 484 848 486(10) = 1 0001 0101 1010 1011 1110 0110 1010 1011 1000 1001 0011 0110 0110(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 53.
A signed binary's bit length must be equal to a power of 2, as of:
21 = 2; 22 = 4; 23 = 8; 24 = 16; 25 = 32; 26 = 64; ...
The first bit (the leftmost) is reserved for the sign:
0 = positive integer number, 1 = negative integer number
The least number that is:
1) a power of 2
2) and is larger than the actual length, 53,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 64.
4. Get the positive binary computer representation on 64 bits (8 Bytes):
If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 64:
Number 4 884 848 484 848 486(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
4 884 848 484 848 486(10) = 0000 0000 0001 0001 0101 1010 1011 1110 0110 1010 1011 1000 1001 0011 0110 0110
Spaces were used to group digits: for binary, by 4, for decimal, by 3.