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;
- 11 111 002 ÷ 2 = 5 555 501 + 0;
- 5 555 501 ÷ 2 = 2 777 750 + 1;
- 2 777 750 ÷ 2 = 1 388 875 + 0;
- 1 388 875 ÷ 2 = 694 437 + 1;
- 694 437 ÷ 2 = 347 218 + 1;
- 347 218 ÷ 2 = 173 609 + 0;
- 173 609 ÷ 2 = 86 804 + 1;
- 86 804 ÷ 2 = 43 402 + 0;
- 43 402 ÷ 2 = 21 701 + 0;
- 21 701 ÷ 2 = 10 850 + 1;
- 10 850 ÷ 2 = 5 425 + 0;
- 5 425 ÷ 2 = 2 712 + 1;
- 2 712 ÷ 2 = 1 356 + 0;
- 1 356 ÷ 2 = 678 + 0;
- 678 ÷ 2 = 339 + 0;
- 339 ÷ 2 = 169 + 1;
- 169 ÷ 2 = 84 + 1;
- 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.
11 111 002(10) = 1010 1001 1000 1010 0101 1010(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 11 111 002(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
11 111 002(10) = 0000 0000 1010 1001 1000 1010 0101 1010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.