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;
- 11 011 001 011 084 ÷ 2 = 5 505 500 505 542 + 0;
- 5 505 500 505 542 ÷ 2 = 2 752 750 252 771 + 0;
- 2 752 750 252 771 ÷ 2 = 1 376 375 126 385 + 1;
- 1 376 375 126 385 ÷ 2 = 688 187 563 192 + 1;
- 688 187 563 192 ÷ 2 = 344 093 781 596 + 0;
- 344 093 781 596 ÷ 2 = 172 046 890 798 + 0;
- 172 046 890 798 ÷ 2 = 86 023 445 399 + 0;
- 86 023 445 399 ÷ 2 = 43 011 722 699 + 1;
- 43 011 722 699 ÷ 2 = 21 505 861 349 + 1;
- 21 505 861 349 ÷ 2 = 10 752 930 674 + 1;
- 10 752 930 674 ÷ 2 = 5 376 465 337 + 0;
- 5 376 465 337 ÷ 2 = 2 688 232 668 + 1;
- 2 688 232 668 ÷ 2 = 1 344 116 334 + 0;
- 1 344 116 334 ÷ 2 = 672 058 167 + 0;
- 672 058 167 ÷ 2 = 336 029 083 + 1;
- 336 029 083 ÷ 2 = 168 014 541 + 1;
- 168 014 541 ÷ 2 = 84 007 270 + 1;
- 84 007 270 ÷ 2 = 42 003 635 + 0;
- 42 003 635 ÷ 2 = 21 001 817 + 1;
- 21 001 817 ÷ 2 = 10 500 908 + 1;
- 10 500 908 ÷ 2 = 5 250 454 + 0;
- 5 250 454 ÷ 2 = 2 625 227 + 0;
- 2 625 227 ÷ 2 = 1 312 613 + 1;
- 1 312 613 ÷ 2 = 656 306 + 1;
- 656 306 ÷ 2 = 328 153 + 0;
- 328 153 ÷ 2 = 164 076 + 1;
- 164 076 ÷ 2 = 82 038 + 0;
- 82 038 ÷ 2 = 41 019 + 0;
- 41 019 ÷ 2 = 20 509 + 1;
- 20 509 ÷ 2 = 10 254 + 1;
- 10 254 ÷ 2 = 5 127 + 0;
- 5 127 ÷ 2 = 2 563 + 1;
- 2 563 ÷ 2 = 1 281 + 1;
- 1 281 ÷ 2 = 640 + 1;
- 640 ÷ 2 = 320 + 0;
- 320 ÷ 2 = 160 + 0;
- 160 ÷ 2 = 80 + 0;
- 80 ÷ 2 = 40 + 0;
- 40 ÷ 2 = 20 + 0;
- 20 ÷ 2 = 10 + 0;
- 10 ÷ 2 = 5 + 0;
- 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.
11 011 001 011 084(10) = 1010 0000 0011 1011 0010 1100 1101 1100 1011 1000 1100(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 44.
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, 44,
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 11 011 001 011 084(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:
11 011 001 011 084(10) = 0000 0000 0000 0000 0000 1010 0000 0011 1011 0010 1100 1101 1100 1011 1000 1100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.