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;
- 11 010 109 ÷ 2 = 5 505 054 + 1;
- 5 505 054 ÷ 2 = 2 752 527 + 0;
- 2 752 527 ÷ 2 = 1 376 263 + 1;
- 1 376 263 ÷ 2 = 688 131 + 1;
- 688 131 ÷ 2 = 344 065 + 1;
- 344 065 ÷ 2 = 172 032 + 1;
- 172 032 ÷ 2 = 86 016 + 0;
- 86 016 ÷ 2 = 43 008 + 0;
- 43 008 ÷ 2 = 21 504 + 0;
- 21 504 ÷ 2 = 10 752 + 0;
- 10 752 ÷ 2 = 5 376 + 0;
- 5 376 ÷ 2 = 2 688 + 0;
- 2 688 ÷ 2 = 1 344 + 0;
- 1 344 ÷ 2 = 672 + 0;
- 672 ÷ 2 = 336 + 0;
- 336 ÷ 2 = 168 + 0;
- 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.
11 010 109(10) = 1010 1000 0000 0000 0011 1101(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) 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, 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 11 010 109(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:
11 010 109(10) = 0000 0000 1010 1000 0000 0000 0011 1101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.