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;
- 1 110 101 011 012 ÷ 2 = 555 050 505 506 + 0;
- 555 050 505 506 ÷ 2 = 277 525 252 753 + 0;
- 277 525 252 753 ÷ 2 = 138 762 626 376 + 1;
- 138 762 626 376 ÷ 2 = 69 381 313 188 + 0;
- 69 381 313 188 ÷ 2 = 34 690 656 594 + 0;
- 34 690 656 594 ÷ 2 = 17 345 328 297 + 0;
- 17 345 328 297 ÷ 2 = 8 672 664 148 + 1;
- 8 672 664 148 ÷ 2 = 4 336 332 074 + 0;
- 4 336 332 074 ÷ 2 = 2 168 166 037 + 0;
- 2 168 166 037 ÷ 2 = 1 084 083 018 + 1;
- 1 084 083 018 ÷ 2 = 542 041 509 + 0;
- 542 041 509 ÷ 2 = 271 020 754 + 1;
- 271 020 754 ÷ 2 = 135 510 377 + 0;
- 135 510 377 ÷ 2 = 67 755 188 + 1;
- 67 755 188 ÷ 2 = 33 877 594 + 0;
- 33 877 594 ÷ 2 = 16 938 797 + 0;
- 16 938 797 ÷ 2 = 8 469 398 + 1;
- 8 469 398 ÷ 2 = 4 234 699 + 0;
- 4 234 699 ÷ 2 = 2 117 349 + 1;
- 2 117 349 ÷ 2 = 1 058 674 + 1;
- 1 058 674 ÷ 2 = 529 337 + 0;
- 529 337 ÷ 2 = 264 668 + 1;
- 264 668 ÷ 2 = 132 334 + 0;
- 132 334 ÷ 2 = 66 167 + 0;
- 66 167 ÷ 2 = 33 083 + 1;
- 33 083 ÷ 2 = 16 541 + 1;
- 16 541 ÷ 2 = 8 270 + 1;
- 8 270 ÷ 2 = 4 135 + 0;
- 4 135 ÷ 2 = 2 067 + 1;
- 2 067 ÷ 2 = 1 033 + 1;
- 1 033 ÷ 2 = 516 + 1;
- 516 ÷ 2 = 258 + 0;
- 258 ÷ 2 = 129 + 0;
- 129 ÷ 2 = 64 + 1;
- 64 ÷ 2 = 32 + 0;
- 32 ÷ 2 = 16 + 0;
- 16 ÷ 2 = 8 + 0;
- 8 ÷ 2 = 4 + 0;
- 4 ÷ 2 = 2 + 0;
- 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.
1 110 101 011 012(10) = 1 0000 0010 0111 0111 0010 1101 0010 1010 0100 0100(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 41.
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, 41,
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 1 110 101 011 012(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:
1 110 101 011 012(10) = 0000 0000 0000 0000 0000 0001 0000 0010 0111 0111 0010 1101 0010 1010 0100 0100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.