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;
- 11 111 111 034 ÷ 2 = 5 555 555 517 + 0;
- 5 555 555 517 ÷ 2 = 2 777 777 758 + 1;
- 2 777 777 758 ÷ 2 = 1 388 888 879 + 0;
- 1 388 888 879 ÷ 2 = 694 444 439 + 1;
- 694 444 439 ÷ 2 = 347 222 219 + 1;
- 347 222 219 ÷ 2 = 173 611 109 + 1;
- 173 611 109 ÷ 2 = 86 805 554 + 1;
- 86 805 554 ÷ 2 = 43 402 777 + 0;
- 43 402 777 ÷ 2 = 21 701 388 + 1;
- 21 701 388 ÷ 2 = 10 850 694 + 0;
- 10 850 694 ÷ 2 = 5 425 347 + 0;
- 5 425 347 ÷ 2 = 2 712 673 + 1;
- 2 712 673 ÷ 2 = 1 356 336 + 1;
- 1 356 336 ÷ 2 = 678 168 + 0;
- 678 168 ÷ 2 = 339 084 + 0;
- 339 084 ÷ 2 = 169 542 + 0;
- 169 542 ÷ 2 = 84 771 + 0;
- 84 771 ÷ 2 = 42 385 + 1;
- 42 385 ÷ 2 = 21 192 + 1;
- 21 192 ÷ 2 = 10 596 + 0;
- 10 596 ÷ 2 = 5 298 + 0;
- 5 298 ÷ 2 = 2 649 + 0;
- 2 649 ÷ 2 = 1 324 + 1;
- 1 324 ÷ 2 = 662 + 0;
- 662 ÷ 2 = 331 + 0;
- 331 ÷ 2 = 165 + 1;
- 165 ÷ 2 = 82 + 1;
- 82 ÷ 2 = 41 + 0;
- 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.
11 111 111 034(10) = 10 1001 0110 0100 0110 0001 1001 0111 1010(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 34.
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, 34,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 64.
4. Get the positive binary computer representation on 64 bits (8 Bytes):
If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 64:
Number 11 111 111 034(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
11 111 111 034(10) = 0000 0000 0000 0000 0000 0000 0000 0010 1001 0110 0100 0110 0001 1001 0111 1010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.