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;
- 765 229 409 ÷ 2 = 382 614 704 + 1;
- 382 614 704 ÷ 2 = 191 307 352 + 0;
- 191 307 352 ÷ 2 = 95 653 676 + 0;
- 95 653 676 ÷ 2 = 47 826 838 + 0;
- 47 826 838 ÷ 2 = 23 913 419 + 0;
- 23 913 419 ÷ 2 = 11 956 709 + 1;
- 11 956 709 ÷ 2 = 5 978 354 + 1;
- 5 978 354 ÷ 2 = 2 989 177 + 0;
- 2 989 177 ÷ 2 = 1 494 588 + 1;
- 1 494 588 ÷ 2 = 747 294 + 0;
- 747 294 ÷ 2 = 373 647 + 0;
- 373 647 ÷ 2 = 186 823 + 1;
- 186 823 ÷ 2 = 93 411 + 1;
- 93 411 ÷ 2 = 46 705 + 1;
- 46 705 ÷ 2 = 23 352 + 1;
- 23 352 ÷ 2 = 11 676 + 0;
- 11 676 ÷ 2 = 5 838 + 0;
- 5 838 ÷ 2 = 2 919 + 0;
- 2 919 ÷ 2 = 1 459 + 1;
- 1 459 ÷ 2 = 729 + 1;
- 729 ÷ 2 = 364 + 1;
- 364 ÷ 2 = 182 + 0;
- 182 ÷ 2 = 91 + 0;
- 91 ÷ 2 = 45 + 1;
- 45 ÷ 2 = 22 + 1;
- 22 ÷ 2 = 11 + 0;
- 11 ÷ 2 = 5 + 1;
- 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.
765 229 409(10) = 10 1101 1001 1100 0111 1001 0110 0001(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 30.
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, 30,
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 765 229 409(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
765 229 409(10) = 0010 1101 1001 1100 0111 1001 0110 0001
Spaces were used to group digits: for binary, by 4, for decimal, by 3.