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;
- 57 318 479 491 ÷ 2 = 28 659 239 745 + 1;
- 28 659 239 745 ÷ 2 = 14 329 619 872 + 1;
- 14 329 619 872 ÷ 2 = 7 164 809 936 + 0;
- 7 164 809 936 ÷ 2 = 3 582 404 968 + 0;
- 3 582 404 968 ÷ 2 = 1 791 202 484 + 0;
- 1 791 202 484 ÷ 2 = 895 601 242 + 0;
- 895 601 242 ÷ 2 = 447 800 621 + 0;
- 447 800 621 ÷ 2 = 223 900 310 + 1;
- 223 900 310 ÷ 2 = 111 950 155 + 0;
- 111 950 155 ÷ 2 = 55 975 077 + 1;
- 55 975 077 ÷ 2 = 27 987 538 + 1;
- 27 987 538 ÷ 2 = 13 993 769 + 0;
- 13 993 769 ÷ 2 = 6 996 884 + 1;
- 6 996 884 ÷ 2 = 3 498 442 + 0;
- 3 498 442 ÷ 2 = 1 749 221 + 0;
- 1 749 221 ÷ 2 = 874 610 + 1;
- 874 610 ÷ 2 = 437 305 + 0;
- 437 305 ÷ 2 = 218 652 + 1;
- 218 652 ÷ 2 = 109 326 + 0;
- 109 326 ÷ 2 = 54 663 + 0;
- 54 663 ÷ 2 = 27 331 + 1;
- 27 331 ÷ 2 = 13 665 + 1;
- 13 665 ÷ 2 = 6 832 + 1;
- 6 832 ÷ 2 = 3 416 + 0;
- 3 416 ÷ 2 = 1 708 + 0;
- 1 708 ÷ 2 = 854 + 0;
- 854 ÷ 2 = 427 + 0;
- 427 ÷ 2 = 213 + 1;
- 213 ÷ 2 = 106 + 1;
- 106 ÷ 2 = 53 + 0;
- 53 ÷ 2 = 26 + 1;
- 26 ÷ 2 = 13 + 0;
- 13 ÷ 2 = 6 + 1;
- 6 ÷ 2 = 3 + 0;
- 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.
57 318 479 491(10) = 1101 0101 1000 0111 0010 1001 0110 1000 0011(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 36.
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, 36,
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 57 318 479 491(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:
57 318 479 491(10) = 0000 0000 0000 0000 0000 0000 0000 1101 0101 1000 0111 0010 1001 0110 1000 0011
Spaces were used to group digits: for binary, by 4, for decimal, by 3.