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;
- 3 758 096 160 ÷ 2 = 1 879 048 080 + 0;
- 1 879 048 080 ÷ 2 = 939 524 040 + 0;
- 939 524 040 ÷ 2 = 469 762 020 + 0;
- 469 762 020 ÷ 2 = 234 881 010 + 0;
- 234 881 010 ÷ 2 = 117 440 505 + 0;
- 117 440 505 ÷ 2 = 58 720 252 + 1;
- 58 720 252 ÷ 2 = 29 360 126 + 0;
- 29 360 126 ÷ 2 = 14 680 063 + 0;
- 14 680 063 ÷ 2 = 7 340 031 + 1;
- 7 340 031 ÷ 2 = 3 670 015 + 1;
- 3 670 015 ÷ 2 = 1 835 007 + 1;
- 1 835 007 ÷ 2 = 917 503 + 1;
- 917 503 ÷ 2 = 458 751 + 1;
- 458 751 ÷ 2 = 229 375 + 1;
- 229 375 ÷ 2 = 114 687 + 1;
- 114 687 ÷ 2 = 57 343 + 1;
- 57 343 ÷ 2 = 28 671 + 1;
- 28 671 ÷ 2 = 14 335 + 1;
- 14 335 ÷ 2 = 7 167 + 1;
- 7 167 ÷ 2 = 3 583 + 1;
- 3 583 ÷ 2 = 1 791 + 1;
- 1 791 ÷ 2 = 895 + 1;
- 895 ÷ 2 = 447 + 1;
- 447 ÷ 2 = 223 + 1;
- 223 ÷ 2 = 111 + 1;
- 111 ÷ 2 = 55 + 1;
- 55 ÷ 2 = 27 + 1;
- 27 ÷ 2 = 13 + 1;
- 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.
3 758 096 160(10) = 1101 1111 1111 1111 1111 1111 0010 0000(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 3 758 096 160(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
3 758 096 160(10) = 0000 0000 0000 0000 0000 0000 0000 0000 1101 1111 1111 1111 1111 1111 0010 0000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.