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;
- 23 082 005 ÷ 2 = 11 541 002 + 1;
- 11 541 002 ÷ 2 = 5 770 501 + 0;
- 5 770 501 ÷ 2 = 2 885 250 + 1;
- 2 885 250 ÷ 2 = 1 442 625 + 0;
- 1 442 625 ÷ 2 = 721 312 + 1;
- 721 312 ÷ 2 = 360 656 + 0;
- 360 656 ÷ 2 = 180 328 + 0;
- 180 328 ÷ 2 = 90 164 + 0;
- 90 164 ÷ 2 = 45 082 + 0;
- 45 082 ÷ 2 = 22 541 + 0;
- 22 541 ÷ 2 = 11 270 + 1;
- 11 270 ÷ 2 = 5 635 + 0;
- 5 635 ÷ 2 = 2 817 + 1;
- 2 817 ÷ 2 = 1 408 + 1;
- 1 408 ÷ 2 = 704 + 0;
- 704 ÷ 2 = 352 + 0;
- 352 ÷ 2 = 176 + 0;
- 176 ÷ 2 = 88 + 0;
- 88 ÷ 2 = 44 + 0;
- 44 ÷ 2 = 22 + 0;
- 22 ÷ 2 = 11 + 0;
- 11 ÷ 2 = 5 + 1;
- 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.
23 082 005(10) = 1 0110 0000 0011 0100 0001 0101(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 25.
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, 25,
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 23 082 005(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
23 082 005(10) = 0000 0001 0110 0000 0011 0100 0001 0101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.