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;
- 8 656 027 ÷ 2 = 4 328 013 + 1;
- 4 328 013 ÷ 2 = 2 164 006 + 1;
- 2 164 006 ÷ 2 = 1 082 003 + 0;
- 1 082 003 ÷ 2 = 541 001 + 1;
- 541 001 ÷ 2 = 270 500 + 1;
- 270 500 ÷ 2 = 135 250 + 0;
- 135 250 ÷ 2 = 67 625 + 0;
- 67 625 ÷ 2 = 33 812 + 1;
- 33 812 ÷ 2 = 16 906 + 0;
- 16 906 ÷ 2 = 8 453 + 0;
- 8 453 ÷ 2 = 4 226 + 1;
- 4 226 ÷ 2 = 2 113 + 0;
- 2 113 ÷ 2 = 1 056 + 1;
- 1 056 ÷ 2 = 528 + 0;
- 528 ÷ 2 = 264 + 0;
- 264 ÷ 2 = 132 + 0;
- 132 ÷ 2 = 66 + 0;
- 66 ÷ 2 = 33 + 0;
- 33 ÷ 2 = 16 + 1;
- 16 ÷ 2 = 8 + 0;
- 8 ÷ 2 = 4 + 0;
- 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.
8 656 027(10) = 1000 0100 0001 0100 1001 1011(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 24.
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, 24,
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 8 656 027(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
8 656 027(10) = 0000 0000 1000 0100 0001 0100 1001 1011
Spaces were used to group digits: for binary, by 4, for decimal, by 3.