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;
- 11 100 011 108 ÷ 2 = 5 550 005 554 + 0;
- 5 550 005 554 ÷ 2 = 2 775 002 777 + 0;
- 2 775 002 777 ÷ 2 = 1 387 501 388 + 1;
- 1 387 501 388 ÷ 2 = 693 750 694 + 0;
- 693 750 694 ÷ 2 = 346 875 347 + 0;
- 346 875 347 ÷ 2 = 173 437 673 + 1;
- 173 437 673 ÷ 2 = 86 718 836 + 1;
- 86 718 836 ÷ 2 = 43 359 418 + 0;
- 43 359 418 ÷ 2 = 21 679 709 + 0;
- 21 679 709 ÷ 2 = 10 839 854 + 1;
- 10 839 854 ÷ 2 = 5 419 927 + 0;
- 5 419 927 ÷ 2 = 2 709 963 + 1;
- 2 709 963 ÷ 2 = 1 354 981 + 1;
- 1 354 981 ÷ 2 = 677 490 + 1;
- 677 490 ÷ 2 = 338 745 + 0;
- 338 745 ÷ 2 = 169 372 + 1;
- 169 372 ÷ 2 = 84 686 + 0;
- 84 686 ÷ 2 = 42 343 + 0;
- 42 343 ÷ 2 = 21 171 + 1;
- 21 171 ÷ 2 = 10 585 + 1;
- 10 585 ÷ 2 = 5 292 + 1;
- 5 292 ÷ 2 = 2 646 + 0;
- 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.
11 100 011 108(10) = 10 1001 0101 1001 1100 1011 1010 0110 0100(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 11 100 011 108(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:
11 100 011 108(10) = 0000 0000 0000 0000 0000 0000 0000 0010 1001 0101 1001 1100 1011 1010 0110 0100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.