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;
- 100 099 999 893 ÷ 2 = 50 049 999 946 + 1;
- 50 049 999 946 ÷ 2 = 25 024 999 973 + 0;
- 25 024 999 973 ÷ 2 = 12 512 499 986 + 1;
- 12 512 499 986 ÷ 2 = 6 256 249 993 + 0;
- 6 256 249 993 ÷ 2 = 3 128 124 996 + 1;
- 3 128 124 996 ÷ 2 = 1 564 062 498 + 0;
- 1 564 062 498 ÷ 2 = 782 031 249 + 0;
- 782 031 249 ÷ 2 = 391 015 624 + 1;
- 391 015 624 ÷ 2 = 195 507 812 + 0;
- 195 507 812 ÷ 2 = 97 753 906 + 0;
- 97 753 906 ÷ 2 = 48 876 953 + 0;
- 48 876 953 ÷ 2 = 24 438 476 + 1;
- 24 438 476 ÷ 2 = 12 219 238 + 0;
- 12 219 238 ÷ 2 = 6 109 619 + 0;
- 6 109 619 ÷ 2 = 3 054 809 + 1;
- 3 054 809 ÷ 2 = 1 527 404 + 1;
- 1 527 404 ÷ 2 = 763 702 + 0;
- 763 702 ÷ 2 = 381 851 + 0;
- 381 851 ÷ 2 = 190 925 + 1;
- 190 925 ÷ 2 = 95 462 + 1;
- 95 462 ÷ 2 = 47 731 + 0;
- 47 731 ÷ 2 = 23 865 + 1;
- 23 865 ÷ 2 = 11 932 + 1;
- 11 932 ÷ 2 = 5 966 + 0;
- 5 966 ÷ 2 = 2 983 + 0;
- 2 983 ÷ 2 = 1 491 + 1;
- 1 491 ÷ 2 = 745 + 1;
- 745 ÷ 2 = 372 + 1;
- 372 ÷ 2 = 186 + 0;
- 186 ÷ 2 = 93 + 0;
- 93 ÷ 2 = 46 + 1;
- 46 ÷ 2 = 23 + 0;
- 23 ÷ 2 = 11 + 1;
- 11 ÷ 2 = 5 + 1;
- 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.
100 099 999 893(10) = 1 0111 0100 1110 0110 1100 1100 1000 1001 0101(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 37.
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, 37,
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 100 099 999 893(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in one's complement representation:
100 099 999 893(10) = 0000 0000 0000 0000 0000 0000 0001 0111 0100 1110 0110 1100 1100 1000 1001 0101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.