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;
- 453 558 924 ÷ 2 = 226 779 462 + 0;
- 226 779 462 ÷ 2 = 113 389 731 + 0;
- 113 389 731 ÷ 2 = 56 694 865 + 1;
- 56 694 865 ÷ 2 = 28 347 432 + 1;
- 28 347 432 ÷ 2 = 14 173 716 + 0;
- 14 173 716 ÷ 2 = 7 086 858 + 0;
- 7 086 858 ÷ 2 = 3 543 429 + 0;
- 3 543 429 ÷ 2 = 1 771 714 + 1;
- 1 771 714 ÷ 2 = 885 857 + 0;
- 885 857 ÷ 2 = 442 928 + 1;
- 442 928 ÷ 2 = 221 464 + 0;
- 221 464 ÷ 2 = 110 732 + 0;
- 110 732 ÷ 2 = 55 366 + 0;
- 55 366 ÷ 2 = 27 683 + 0;
- 27 683 ÷ 2 = 13 841 + 1;
- 13 841 ÷ 2 = 6 920 + 1;
- 6 920 ÷ 2 = 3 460 + 0;
- 3 460 ÷ 2 = 1 730 + 0;
- 1 730 ÷ 2 = 865 + 0;
- 865 ÷ 2 = 432 + 1;
- 432 ÷ 2 = 216 + 0;
- 216 ÷ 2 = 108 + 0;
- 108 ÷ 2 = 54 + 0;
- 54 ÷ 2 = 27 + 0;
- 27 ÷ 2 = 13 + 1;
- 13 ÷ 2 = 6 + 1;
- 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.
453 558 924(10) = 1 1011 0000 1000 1100 0010 1000 1100(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 29.
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, 29,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 32.
4. Get the positive binary computer representation on 32 bits (4 Bytes):
If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 32.
Number 453 558 924(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:
453 558 924(10) = 0001 1011 0000 1000 1100 0010 1000 1100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.