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;
- 111 110 011 113 ÷ 2 = 55 555 005 556 + 1;
- 55 555 005 556 ÷ 2 = 27 777 502 778 + 0;
- 27 777 502 778 ÷ 2 = 13 888 751 389 + 0;
- 13 888 751 389 ÷ 2 = 6 944 375 694 + 1;
- 6 944 375 694 ÷ 2 = 3 472 187 847 + 0;
- 3 472 187 847 ÷ 2 = 1 736 093 923 + 1;
- 1 736 093 923 ÷ 2 = 868 046 961 + 1;
- 868 046 961 ÷ 2 = 434 023 480 + 1;
- 434 023 480 ÷ 2 = 217 011 740 + 0;
- 217 011 740 ÷ 2 = 108 505 870 + 0;
- 108 505 870 ÷ 2 = 54 252 935 + 0;
- 54 252 935 ÷ 2 = 27 126 467 + 1;
- 27 126 467 ÷ 2 = 13 563 233 + 1;
- 13 563 233 ÷ 2 = 6 781 616 + 1;
- 6 781 616 ÷ 2 = 3 390 808 + 0;
- 3 390 808 ÷ 2 = 1 695 404 + 0;
- 1 695 404 ÷ 2 = 847 702 + 0;
- 847 702 ÷ 2 = 423 851 + 0;
- 423 851 ÷ 2 = 211 925 + 1;
- 211 925 ÷ 2 = 105 962 + 1;
- 105 962 ÷ 2 = 52 981 + 0;
- 52 981 ÷ 2 = 26 490 + 1;
- 26 490 ÷ 2 = 13 245 + 0;
- 13 245 ÷ 2 = 6 622 + 1;
- 6 622 ÷ 2 = 3 311 + 0;
- 3 311 ÷ 2 = 1 655 + 1;
- 1 655 ÷ 2 = 827 + 1;
- 827 ÷ 2 = 413 + 1;
- 413 ÷ 2 = 206 + 1;
- 206 ÷ 2 = 103 + 0;
- 103 ÷ 2 = 51 + 1;
- 51 ÷ 2 = 25 + 1;
- 25 ÷ 2 = 12 + 1;
- 12 ÷ 2 = 6 + 0;
- 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.
111 110 011 113(10) = 1 1001 1101 1110 1010 1100 0011 1000 1110 1001(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 111 110 011 113(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
111 110 011 113(10) = 0000 0000 0000 0000 0000 0000 0001 1001 1101 1110 1010 1100 0011 1000 1110 1001
Spaces were used to group digits: for binary, by 4, for decimal, by 3.