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;
- 8 659 380 886 ÷ 2 = 4 329 690 443 + 0;
- 4 329 690 443 ÷ 2 = 2 164 845 221 + 1;
- 2 164 845 221 ÷ 2 = 1 082 422 610 + 1;
- 1 082 422 610 ÷ 2 = 541 211 305 + 0;
- 541 211 305 ÷ 2 = 270 605 652 + 1;
- 270 605 652 ÷ 2 = 135 302 826 + 0;
- 135 302 826 ÷ 2 = 67 651 413 + 0;
- 67 651 413 ÷ 2 = 33 825 706 + 1;
- 33 825 706 ÷ 2 = 16 912 853 + 0;
- 16 912 853 ÷ 2 = 8 456 426 + 1;
- 8 456 426 ÷ 2 = 4 228 213 + 0;
- 4 228 213 ÷ 2 = 2 114 106 + 1;
- 2 114 106 ÷ 2 = 1 057 053 + 0;
- 1 057 053 ÷ 2 = 528 526 + 1;
- 528 526 ÷ 2 = 264 263 + 0;
- 264 263 ÷ 2 = 132 131 + 1;
- 132 131 ÷ 2 = 66 065 + 1;
- 66 065 ÷ 2 = 33 032 + 1;
- 33 032 ÷ 2 = 16 516 + 0;
- 16 516 ÷ 2 = 8 258 + 0;
- 8 258 ÷ 2 = 4 129 + 0;
- 4 129 ÷ 2 = 2 064 + 1;
- 2 064 ÷ 2 = 1 032 + 0;
- 1 032 ÷ 2 = 516 + 0;
- 516 ÷ 2 = 258 + 0;
- 258 ÷ 2 = 129 + 0;
- 129 ÷ 2 = 64 + 1;
- 64 ÷ 2 = 32 + 0;
- 32 ÷ 2 = 16 + 0;
- 16 ÷ 2 = 8 + 0;
- 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.
8 659 380 886(10) = 10 0000 0100 0010 0011 1010 1010 1001 0110(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 34.
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, 34,
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 8 659 380 886(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:
8 659 380 886(10) = 0000 0000 0000 0000 0000 0000 0000 0010 0000 0100 0010 0011 1010 1010 1001 0110
Spaces were used to group digits: for binary, by 4, for decimal, by 3.