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;
- 22 102 035 ÷ 2 = 11 051 017 + 1;
- 11 051 017 ÷ 2 = 5 525 508 + 1;
- 5 525 508 ÷ 2 = 2 762 754 + 0;
- 2 762 754 ÷ 2 = 1 381 377 + 0;
- 1 381 377 ÷ 2 = 690 688 + 1;
- 690 688 ÷ 2 = 345 344 + 0;
- 345 344 ÷ 2 = 172 672 + 0;
- 172 672 ÷ 2 = 86 336 + 0;
- 86 336 ÷ 2 = 43 168 + 0;
- 43 168 ÷ 2 = 21 584 + 0;
- 21 584 ÷ 2 = 10 792 + 0;
- 10 792 ÷ 2 = 5 396 + 0;
- 5 396 ÷ 2 = 2 698 + 0;
- 2 698 ÷ 2 = 1 349 + 0;
- 1 349 ÷ 2 = 674 + 1;
- 674 ÷ 2 = 337 + 0;
- 337 ÷ 2 = 168 + 1;
- 168 ÷ 2 = 84 + 0;
- 84 ÷ 2 = 42 + 0;
- 42 ÷ 2 = 21 + 0;
- 21 ÷ 2 = 10 + 1;
- 10 ÷ 2 = 5 + 0;
- 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.
22 102 035(10) = 1 0101 0001 0100 0000 0001 0011(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 22 102 035(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
22 102 035(10) = 0000 0001 0101 0001 0100 0000 0001 0011
Spaces were used to group digits: for binary, by 4, for decimal, by 3.