2. 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;
- 1 888 999 333 ÷ 2 = 944 499 666 + 1;
- 944 499 666 ÷ 2 = 472 249 833 + 0;
- 472 249 833 ÷ 2 = 236 124 916 + 1;
- 236 124 916 ÷ 2 = 118 062 458 + 0;
- 118 062 458 ÷ 2 = 59 031 229 + 0;
- 59 031 229 ÷ 2 = 29 515 614 + 1;
- 29 515 614 ÷ 2 = 14 757 807 + 0;
- 14 757 807 ÷ 2 = 7 378 903 + 1;
- 7 378 903 ÷ 2 = 3 689 451 + 1;
- 3 689 451 ÷ 2 = 1 844 725 + 1;
- 1 844 725 ÷ 2 = 922 362 + 1;
- 922 362 ÷ 2 = 461 181 + 0;
- 461 181 ÷ 2 = 230 590 + 1;
- 230 590 ÷ 2 = 115 295 + 0;
- 115 295 ÷ 2 = 57 647 + 1;
- 57 647 ÷ 2 = 28 823 + 1;
- 28 823 ÷ 2 = 14 411 + 1;
- 14 411 ÷ 2 = 7 205 + 1;
- 7 205 ÷ 2 = 3 602 + 1;
- 3 602 ÷ 2 = 1 801 + 0;
- 1 801 ÷ 2 = 900 + 1;
- 900 ÷ 2 = 450 + 0;
- 450 ÷ 2 = 225 + 0;
- 225 ÷ 2 = 112 + 1;
- 112 ÷ 2 = 56 + 0;
- 56 ÷ 2 = 28 + 0;
- 28 ÷ 2 = 14 + 0;
- 14 ÷ 2 = 7 + 0;
- 7 ÷ 2 = 3 + 1;
- 3 ÷ 2 = 1 + 1;
- 1 ÷ 2 = 0 + 1;
3. Construct the base 2 representation of the positive number:
Take all the remainders starting from the bottom of the list constructed above.
1 888 999 333(10) = 111 0000 1001 0111 1101 0111 1010 0101(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 31.
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) is reserved for 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, 31,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 32.
5. 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:
1 888 999 333(10) = 0111 0000 1001 0111 1101 0111 1010 0101
6. Get the negative integer number representation:
To get the negative integer number representation on 32 bits (4 Bytes),
... change the first bit (the leftmost), from 0 to 1...
Number -1 888 999 333(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-1 888 999 333(10) = 1111 0000 1001 0111 1101 0111 1010 0101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.