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;
- 271 362 650 271 888 ÷ 2 = 135 681 325 135 944 + 0;
- 135 681 325 135 944 ÷ 2 = 67 840 662 567 972 + 0;
- 67 840 662 567 972 ÷ 2 = 33 920 331 283 986 + 0;
- 33 920 331 283 986 ÷ 2 = 16 960 165 641 993 + 0;
- 16 960 165 641 993 ÷ 2 = 8 480 082 820 996 + 1;
- 8 480 082 820 996 ÷ 2 = 4 240 041 410 498 + 0;
- 4 240 041 410 498 ÷ 2 = 2 120 020 705 249 + 0;
- 2 120 020 705 249 ÷ 2 = 1 060 010 352 624 + 1;
- 1 060 010 352 624 ÷ 2 = 530 005 176 312 + 0;
- 530 005 176 312 ÷ 2 = 265 002 588 156 + 0;
- 265 002 588 156 ÷ 2 = 132 501 294 078 + 0;
- 132 501 294 078 ÷ 2 = 66 250 647 039 + 0;
- 66 250 647 039 ÷ 2 = 33 125 323 519 + 1;
- 33 125 323 519 ÷ 2 = 16 562 661 759 + 1;
- 16 562 661 759 ÷ 2 = 8 281 330 879 + 1;
- 8 281 330 879 ÷ 2 = 4 140 665 439 + 1;
- 4 140 665 439 ÷ 2 = 2 070 332 719 + 1;
- 2 070 332 719 ÷ 2 = 1 035 166 359 + 1;
- 1 035 166 359 ÷ 2 = 517 583 179 + 1;
- 517 583 179 ÷ 2 = 258 791 589 + 1;
- 258 791 589 ÷ 2 = 129 395 794 + 1;
- 129 395 794 ÷ 2 = 64 697 897 + 0;
- 64 697 897 ÷ 2 = 32 348 948 + 1;
- 32 348 948 ÷ 2 = 16 174 474 + 0;
- 16 174 474 ÷ 2 = 8 087 237 + 0;
- 8 087 237 ÷ 2 = 4 043 618 + 1;
- 4 043 618 ÷ 2 = 2 021 809 + 0;
- 2 021 809 ÷ 2 = 1 010 904 + 1;
- 1 010 904 ÷ 2 = 505 452 + 0;
- 505 452 ÷ 2 = 252 726 + 0;
- 252 726 ÷ 2 = 126 363 + 0;
- 126 363 ÷ 2 = 63 181 + 1;
- 63 181 ÷ 2 = 31 590 + 1;
- 31 590 ÷ 2 = 15 795 + 0;
- 15 795 ÷ 2 = 7 897 + 1;
- 7 897 ÷ 2 = 3 948 + 1;
- 3 948 ÷ 2 = 1 974 + 0;
- 1 974 ÷ 2 = 987 + 0;
- 987 ÷ 2 = 493 + 1;
- 493 ÷ 2 = 246 + 1;
- 246 ÷ 2 = 123 + 0;
- 123 ÷ 2 = 61 + 1;
- 61 ÷ 2 = 30 + 1;
- 30 ÷ 2 = 15 + 0;
- 15 ÷ 2 = 7 + 1;
- 7 ÷ 2 = 3 + 1;
- 3 ÷ 2 = 1 + 1;
- 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.
271 362 650 271 888(10) = 1111 0110 1100 1101 1000 1010 0101 1111 1111 0000 1001 0000(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 48.
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, 48,
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 271 362 650 271 888(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
271 362 650 271 888(10) = 0000 0000 0000 0000 1111 0110 1100 1101 1000 1010 0101 1111 1111 0000 1001 0000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.