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;
- 349 780 326 ÷ 2 = 174 890 163 + 0;
- 174 890 163 ÷ 2 = 87 445 081 + 1;
- 87 445 081 ÷ 2 = 43 722 540 + 1;
- 43 722 540 ÷ 2 = 21 861 270 + 0;
- 21 861 270 ÷ 2 = 10 930 635 + 0;
- 10 930 635 ÷ 2 = 5 465 317 + 1;
- 5 465 317 ÷ 2 = 2 732 658 + 1;
- 2 732 658 ÷ 2 = 1 366 329 + 0;
- 1 366 329 ÷ 2 = 683 164 + 1;
- 683 164 ÷ 2 = 341 582 + 0;
- 341 582 ÷ 2 = 170 791 + 0;
- 170 791 ÷ 2 = 85 395 + 1;
- 85 395 ÷ 2 = 42 697 + 1;
- 42 697 ÷ 2 = 21 348 + 1;
- 21 348 ÷ 2 = 10 674 + 0;
- 10 674 ÷ 2 = 5 337 + 0;
- 5 337 ÷ 2 = 2 668 + 1;
- 2 668 ÷ 2 = 1 334 + 0;
- 1 334 ÷ 2 = 667 + 0;
- 667 ÷ 2 = 333 + 1;
- 333 ÷ 2 = 166 + 1;
- 166 ÷ 2 = 83 + 0;
- 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.
349 780 326(10) = 1 0100 1101 1001 0011 1001 0110 0110(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 29.
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, 29,
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 349 780 326(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:
349 780 326(10) = 0001 0100 1101 1001 0011 1001 0110 0110
Spaces were used to group digits: for binary, by 4, for decimal, by 3.