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;
- 11 010 000 ÷ 2 = 5 505 000 + 0;
- 5 505 000 ÷ 2 = 2 752 500 + 0;
- 2 752 500 ÷ 2 = 1 376 250 + 0;
- 1 376 250 ÷ 2 = 688 125 + 0;
- 688 125 ÷ 2 = 344 062 + 1;
- 344 062 ÷ 2 = 172 031 + 0;
- 172 031 ÷ 2 = 86 015 + 1;
- 86 015 ÷ 2 = 43 007 + 1;
- 43 007 ÷ 2 = 21 503 + 1;
- 21 503 ÷ 2 = 10 751 + 1;
- 10 751 ÷ 2 = 5 375 + 1;
- 5 375 ÷ 2 = 2 687 + 1;
- 2 687 ÷ 2 = 1 343 + 1;
- 1 343 ÷ 2 = 671 + 1;
- 671 ÷ 2 = 335 + 1;
- 335 ÷ 2 = 167 + 1;
- 167 ÷ 2 = 83 + 1;
- 83 ÷ 2 = 41 + 1;
- 41 ÷ 2 = 20 + 1;
- 20 ÷ 2 = 10 + 0;
- 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.
11 010 000(10) = 1010 0111 1111 1111 1101 0000(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 11 010 000(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in two's complement representation:
11 010 000(10) = 0000 0000 1010 0111 1111 1111 1101 0000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.