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;
- 318 767 062 ÷ 2 = 159 383 531 + 0;
- 159 383 531 ÷ 2 = 79 691 765 + 1;
- 79 691 765 ÷ 2 = 39 845 882 + 1;
- 39 845 882 ÷ 2 = 19 922 941 + 0;
- 19 922 941 ÷ 2 = 9 961 470 + 1;
- 9 961 470 ÷ 2 = 4 980 735 + 0;
- 4 980 735 ÷ 2 = 2 490 367 + 1;
- 2 490 367 ÷ 2 = 1 245 183 + 1;
- 1 245 183 ÷ 2 = 622 591 + 1;
- 622 591 ÷ 2 = 311 295 + 1;
- 311 295 ÷ 2 = 155 647 + 1;
- 155 647 ÷ 2 = 77 823 + 1;
- 77 823 ÷ 2 = 38 911 + 1;
- 38 911 ÷ 2 = 19 455 + 1;
- 19 455 ÷ 2 = 9 727 + 1;
- 9 727 ÷ 2 = 4 863 + 1;
- 4 863 ÷ 2 = 2 431 + 1;
- 2 431 ÷ 2 = 1 215 + 1;
- 1 215 ÷ 2 = 607 + 1;
- 607 ÷ 2 = 303 + 1;
- 303 ÷ 2 = 151 + 1;
- 151 ÷ 2 = 75 + 1;
- 75 ÷ 2 = 37 + 1;
- 37 ÷ 2 = 18 + 1;
- 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.
318 767 062(10) = 1 0010 1111 1111 1111 1111 1101 0110(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 318 767 062(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:
318 767 062(10) = 0001 0010 1111 1111 1111 1111 1101 0110
Spaces were used to group digits: for binary, by 4, for decimal, by 3.