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;
- 100 111 110 055 ÷ 2 = 50 055 555 027 + 1;
- 50 055 555 027 ÷ 2 = 25 027 777 513 + 1;
- 25 027 777 513 ÷ 2 = 12 513 888 756 + 1;
- 12 513 888 756 ÷ 2 = 6 256 944 378 + 0;
- 6 256 944 378 ÷ 2 = 3 128 472 189 + 0;
- 3 128 472 189 ÷ 2 = 1 564 236 094 + 1;
- 1 564 236 094 ÷ 2 = 782 118 047 + 0;
- 782 118 047 ÷ 2 = 391 059 023 + 1;
- 391 059 023 ÷ 2 = 195 529 511 + 1;
- 195 529 511 ÷ 2 = 97 764 755 + 1;
- 97 764 755 ÷ 2 = 48 882 377 + 1;
- 48 882 377 ÷ 2 = 24 441 188 + 1;
- 24 441 188 ÷ 2 = 12 220 594 + 0;
- 12 220 594 ÷ 2 = 6 110 297 + 0;
- 6 110 297 ÷ 2 = 3 055 148 + 1;
- 3 055 148 ÷ 2 = 1 527 574 + 0;
- 1 527 574 ÷ 2 = 763 787 + 0;
- 763 787 ÷ 2 = 381 893 + 1;
- 381 893 ÷ 2 = 190 946 + 1;
- 190 946 ÷ 2 = 95 473 + 0;
- 95 473 ÷ 2 = 47 736 + 1;
- 47 736 ÷ 2 = 23 868 + 0;
- 23 868 ÷ 2 = 11 934 + 0;
- 11 934 ÷ 2 = 5 967 + 0;
- 5 967 ÷ 2 = 2 983 + 1;
- 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.
100 111 110 055(10) = 1 0111 0100 1111 0001 0110 0100 1111 1010 0111(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) 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, 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 100 111 110 055(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
100 111 110 055(10) = 0000 0000 0000 0000 0000 0000 0001 0111 0100 1111 0001 0110 0100 1111 1010 0111
Spaces were used to group digits: for binary, by 4, for decimal, by 3.