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;
- 111 011 021 ÷ 2 = 55 505 510 + 1;
- 55 505 510 ÷ 2 = 27 752 755 + 0;
- 27 752 755 ÷ 2 = 13 876 377 + 1;
- 13 876 377 ÷ 2 = 6 938 188 + 1;
- 6 938 188 ÷ 2 = 3 469 094 + 0;
- 3 469 094 ÷ 2 = 1 734 547 + 0;
- 1 734 547 ÷ 2 = 867 273 + 1;
- 867 273 ÷ 2 = 433 636 + 1;
- 433 636 ÷ 2 = 216 818 + 0;
- 216 818 ÷ 2 = 108 409 + 0;
- 108 409 ÷ 2 = 54 204 + 1;
- 54 204 ÷ 2 = 27 102 + 0;
- 27 102 ÷ 2 = 13 551 + 0;
- 13 551 ÷ 2 = 6 775 + 1;
- 6 775 ÷ 2 = 3 387 + 1;
- 3 387 ÷ 2 = 1 693 + 1;
- 1 693 ÷ 2 = 846 + 1;
- 846 ÷ 2 = 423 + 0;
- 423 ÷ 2 = 211 + 1;
- 211 ÷ 2 = 105 + 1;
- 105 ÷ 2 = 52 + 1;
- 52 ÷ 2 = 26 + 0;
- 26 ÷ 2 = 13 + 0;
- 13 ÷ 2 = 6 + 1;
- 6 ÷ 2 = 3 + 0;
- 3 ÷ 2 = 1 + 1;
- 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.
111 011 021(10) = 110 1001 1101 1110 0100 1100 1101(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 27.
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, 27,
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 111 011 021(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:
Spaces were used to group digits: for binary, by 4, for decimal, by 3.