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;
- 5 942 326 400 541 ÷ 2 = 2 971 163 200 270 + 1;
- 2 971 163 200 270 ÷ 2 = 1 485 581 600 135 + 0;
- 1 485 581 600 135 ÷ 2 = 742 790 800 067 + 1;
- 742 790 800 067 ÷ 2 = 371 395 400 033 + 1;
- 371 395 400 033 ÷ 2 = 185 697 700 016 + 1;
- 185 697 700 016 ÷ 2 = 92 848 850 008 + 0;
- 92 848 850 008 ÷ 2 = 46 424 425 004 + 0;
- 46 424 425 004 ÷ 2 = 23 212 212 502 + 0;
- 23 212 212 502 ÷ 2 = 11 606 106 251 + 0;
- 11 606 106 251 ÷ 2 = 5 803 053 125 + 1;
- 5 803 053 125 ÷ 2 = 2 901 526 562 + 1;
- 2 901 526 562 ÷ 2 = 1 450 763 281 + 0;
- 1 450 763 281 ÷ 2 = 725 381 640 + 1;
- 725 381 640 ÷ 2 = 362 690 820 + 0;
- 362 690 820 ÷ 2 = 181 345 410 + 0;
- 181 345 410 ÷ 2 = 90 672 705 + 0;
- 90 672 705 ÷ 2 = 45 336 352 + 1;
- 45 336 352 ÷ 2 = 22 668 176 + 0;
- 22 668 176 ÷ 2 = 11 334 088 + 0;
- 11 334 088 ÷ 2 = 5 667 044 + 0;
- 5 667 044 ÷ 2 = 2 833 522 + 0;
- 2 833 522 ÷ 2 = 1 416 761 + 0;
- 1 416 761 ÷ 2 = 708 380 + 1;
- 708 380 ÷ 2 = 354 190 + 0;
- 354 190 ÷ 2 = 177 095 + 0;
- 177 095 ÷ 2 = 88 547 + 1;
- 88 547 ÷ 2 = 44 273 + 1;
- 44 273 ÷ 2 = 22 136 + 1;
- 22 136 ÷ 2 = 11 068 + 0;
- 11 068 ÷ 2 = 5 534 + 0;
- 5 534 ÷ 2 = 2 767 + 0;
- 2 767 ÷ 2 = 1 383 + 1;
- 1 383 ÷ 2 = 691 + 1;
- 691 ÷ 2 = 345 + 1;
- 345 ÷ 2 = 172 + 1;
- 172 ÷ 2 = 86 + 0;
- 86 ÷ 2 = 43 + 0;
- 43 ÷ 2 = 21 + 1;
- 21 ÷ 2 = 10 + 1;
- 10 ÷ 2 = 5 + 0;
- 5 ÷ 2 = 2 + 1;
- 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.
5 942 326 400 541(10) = 101 0110 0111 1000 1110 0100 0001 0001 0110 0001 1101(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 43.
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) indicates 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, 43,
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 5 942 326 400 541(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in two's complement representation:
5 942 326 400 541(10) = 0000 0000 0000 0000 0000 0101 0110 0111 1000 1110 0100 0001 0001 0110 0001 1101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.