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;
- 110 101 088 ÷ 2 = 55 050 544 + 0;
- 55 050 544 ÷ 2 = 27 525 272 + 0;
- 27 525 272 ÷ 2 = 13 762 636 + 0;
- 13 762 636 ÷ 2 = 6 881 318 + 0;
- 6 881 318 ÷ 2 = 3 440 659 + 0;
- 3 440 659 ÷ 2 = 1 720 329 + 1;
- 1 720 329 ÷ 2 = 860 164 + 1;
- 860 164 ÷ 2 = 430 082 + 0;
- 430 082 ÷ 2 = 215 041 + 0;
- 215 041 ÷ 2 = 107 520 + 1;
- 107 520 ÷ 2 = 53 760 + 0;
- 53 760 ÷ 2 = 26 880 + 0;
- 26 880 ÷ 2 = 13 440 + 0;
- 13 440 ÷ 2 = 6 720 + 0;
- 6 720 ÷ 2 = 3 360 + 0;
- 3 360 ÷ 2 = 1 680 + 0;
- 1 680 ÷ 2 = 840 + 0;
- 840 ÷ 2 = 420 + 0;
- 420 ÷ 2 = 210 + 0;
- 210 ÷ 2 = 105 + 0;
- 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.
110 101 088(10) = 110 1001 0000 0000 0010 0110 0000(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 110 101 088(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:
110 101 088(10) = 0000 0110 1001 0000 0000 0010 0110 0000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.