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;
- 2 780 129 981 ÷ 2 = 1 390 064 990 + 1;
- 1 390 064 990 ÷ 2 = 695 032 495 + 0;
- 695 032 495 ÷ 2 = 347 516 247 + 1;
- 347 516 247 ÷ 2 = 173 758 123 + 1;
- 173 758 123 ÷ 2 = 86 879 061 + 1;
- 86 879 061 ÷ 2 = 43 439 530 + 1;
- 43 439 530 ÷ 2 = 21 719 765 + 0;
- 21 719 765 ÷ 2 = 10 859 882 + 1;
- 10 859 882 ÷ 2 = 5 429 941 + 0;
- 5 429 941 ÷ 2 = 2 714 970 + 1;
- 2 714 970 ÷ 2 = 1 357 485 + 0;
- 1 357 485 ÷ 2 = 678 742 + 1;
- 678 742 ÷ 2 = 339 371 + 0;
- 339 371 ÷ 2 = 169 685 + 1;
- 169 685 ÷ 2 = 84 842 + 1;
- 84 842 ÷ 2 = 42 421 + 0;
- 42 421 ÷ 2 = 21 210 + 1;
- 21 210 ÷ 2 = 10 605 + 0;
- 10 605 ÷ 2 = 5 302 + 1;
- 5 302 ÷ 2 = 2 651 + 0;
- 2 651 ÷ 2 = 1 325 + 1;
- 1 325 ÷ 2 = 662 + 1;
- 662 ÷ 2 = 331 + 0;
- 331 ÷ 2 = 165 + 1;
- 165 ÷ 2 = 82 + 1;
- 82 ÷ 2 = 41 + 0;
- 41 ÷ 2 = 20 + 1;
- 20 ÷ 2 = 10 + 0;
- 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.
2 780 129 981(10) = 1010 0101 1011 0101 0110 1010 1011 1101(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) 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, 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 2 780 129 981(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:
2 780 129 981(10) = 0000 0000 0000 0000 0000 0000 0000 0000 1010 0101 1011 0101 0110 1010 1011 1101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.