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;
- 11 101 111 039 ÷ 2 = 5 550 555 519 + 1;
- 5 550 555 519 ÷ 2 = 2 775 277 759 + 1;
- 2 775 277 759 ÷ 2 = 1 387 638 879 + 1;
- 1 387 638 879 ÷ 2 = 693 819 439 + 1;
- 693 819 439 ÷ 2 = 346 909 719 + 1;
- 346 909 719 ÷ 2 = 173 454 859 + 1;
- 173 454 859 ÷ 2 = 86 727 429 + 1;
- 86 727 429 ÷ 2 = 43 363 714 + 1;
- 43 363 714 ÷ 2 = 21 681 857 + 0;
- 21 681 857 ÷ 2 = 10 840 928 + 1;
- 10 840 928 ÷ 2 = 5 420 464 + 0;
- 5 420 464 ÷ 2 = 2 710 232 + 0;
- 2 710 232 ÷ 2 = 1 355 116 + 0;
- 1 355 116 ÷ 2 = 677 558 + 0;
- 677 558 ÷ 2 = 338 779 + 0;
- 338 779 ÷ 2 = 169 389 + 1;
- 169 389 ÷ 2 = 84 694 + 1;
- 84 694 ÷ 2 = 42 347 + 0;
- 42 347 ÷ 2 = 21 173 + 1;
- 21 173 ÷ 2 = 10 586 + 1;
- 10 586 ÷ 2 = 5 293 + 0;
- 5 293 ÷ 2 = 2 646 + 1;
- 2 646 ÷ 2 = 1 323 + 0;
- 1 323 ÷ 2 = 661 + 1;
- 661 ÷ 2 = 330 + 1;
- 330 ÷ 2 = 165 + 0;
- 165 ÷ 2 = 82 + 1;
- 82 ÷ 2 = 41 + 0;
- 41 ÷ 2 = 20 + 1;
- 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.
11 101 111 039(10) = 10 1001 0101 1010 1101 1000 0010 1111 1111(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 34.
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, 34,
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 11 101 111 039(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in two's complement representation:
11 101 111 039(10) = 0000 0000 0000 0000 0000 0000 0000 0010 1001 0101 1010 1101 1000 0010 1111 1111
Spaces were used to group digits: for binary, by 4, for decimal, by 3.