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;
- 307 613 481 ÷ 2 = 153 806 740 + 1;
- 153 806 740 ÷ 2 = 76 903 370 + 0;
- 76 903 370 ÷ 2 = 38 451 685 + 0;
- 38 451 685 ÷ 2 = 19 225 842 + 1;
- 19 225 842 ÷ 2 = 9 612 921 + 0;
- 9 612 921 ÷ 2 = 4 806 460 + 1;
- 4 806 460 ÷ 2 = 2 403 230 + 0;
- 2 403 230 ÷ 2 = 1 201 615 + 0;
- 1 201 615 ÷ 2 = 600 807 + 1;
- 600 807 ÷ 2 = 300 403 + 1;
- 300 403 ÷ 2 = 150 201 + 1;
- 150 201 ÷ 2 = 75 100 + 1;
- 75 100 ÷ 2 = 37 550 + 0;
- 37 550 ÷ 2 = 18 775 + 0;
- 18 775 ÷ 2 = 9 387 + 1;
- 9 387 ÷ 2 = 4 693 + 1;
- 4 693 ÷ 2 = 2 346 + 1;
- 2 346 ÷ 2 = 1 173 + 0;
- 1 173 ÷ 2 = 586 + 1;
- 586 ÷ 2 = 293 + 0;
- 293 ÷ 2 = 146 + 1;
- 146 ÷ 2 = 73 + 0;
- 73 ÷ 2 = 36 + 1;
- 36 ÷ 2 = 18 + 0;
- 18 ÷ 2 = 9 + 0;
- 9 ÷ 2 = 4 + 1;
- 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.
307 613 481(10) = 1 0010 0101 0101 1100 1111 0010 1001(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 307 613 481(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:
307 613 481(10) = 0001 0010 0101 0101 1100 1111 0010 1001
Spaces were used to group digits: for binary, by 4, for decimal, by 3.