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;
- 2 871 999 995 ÷ 2 = 1 435 999 997 + 1;
- 1 435 999 997 ÷ 2 = 717 999 998 + 1;
- 717 999 998 ÷ 2 = 358 999 999 + 0;
- 358 999 999 ÷ 2 = 179 499 999 + 1;
- 179 499 999 ÷ 2 = 89 749 999 + 1;
- 89 749 999 ÷ 2 = 44 874 999 + 1;
- 44 874 999 ÷ 2 = 22 437 499 + 1;
- 22 437 499 ÷ 2 = 11 218 749 + 1;
- 11 218 749 ÷ 2 = 5 609 374 + 1;
- 5 609 374 ÷ 2 = 2 804 687 + 0;
- 2 804 687 ÷ 2 = 1 402 343 + 1;
- 1 402 343 ÷ 2 = 701 171 + 1;
- 701 171 ÷ 2 = 350 585 + 1;
- 350 585 ÷ 2 = 175 292 + 1;
- 175 292 ÷ 2 = 87 646 + 0;
- 87 646 ÷ 2 = 43 823 + 0;
- 43 823 ÷ 2 = 21 911 + 1;
- 21 911 ÷ 2 = 10 955 + 1;
- 10 955 ÷ 2 = 5 477 + 1;
- 5 477 ÷ 2 = 2 738 + 1;
- 2 738 ÷ 2 = 1 369 + 0;
- 1 369 ÷ 2 = 684 + 1;
- 684 ÷ 2 = 342 + 0;
- 342 ÷ 2 = 171 + 0;
- 171 ÷ 2 = 85 + 1;
- 85 ÷ 2 = 42 + 1;
- 42 ÷ 2 = 21 + 0;
- 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.
2 871 999 995(10) = 1010 1011 0010 1111 0011 1101 1111 1011(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 32.
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, 32,
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 2 871 999 995(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
2 871 999 995(10) = 0000 0000 0000 0000 0000 0000 0000 0000 1010 1011 0010 1111 0011 1101 1111 1011
Spaces were used to group digits: for binary, by 4, for decimal, by 3.