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;
- 3 221 225 472 ÷ 2 = 1 610 612 736 + 0;
- 1 610 612 736 ÷ 2 = 805 306 368 + 0;
- 805 306 368 ÷ 2 = 402 653 184 + 0;
- 402 653 184 ÷ 2 = 201 326 592 + 0;
- 201 326 592 ÷ 2 = 100 663 296 + 0;
- 100 663 296 ÷ 2 = 50 331 648 + 0;
- 50 331 648 ÷ 2 = 25 165 824 + 0;
- 25 165 824 ÷ 2 = 12 582 912 + 0;
- 12 582 912 ÷ 2 = 6 291 456 + 0;
- 6 291 456 ÷ 2 = 3 145 728 + 0;
- 3 145 728 ÷ 2 = 1 572 864 + 0;
- 1 572 864 ÷ 2 = 786 432 + 0;
- 786 432 ÷ 2 = 393 216 + 0;
- 393 216 ÷ 2 = 196 608 + 0;
- 196 608 ÷ 2 = 98 304 + 0;
- 98 304 ÷ 2 = 49 152 + 0;
- 49 152 ÷ 2 = 24 576 + 0;
- 24 576 ÷ 2 = 12 288 + 0;
- 12 288 ÷ 2 = 6 144 + 0;
- 6 144 ÷ 2 = 3 072 + 0;
- 3 072 ÷ 2 = 1 536 + 0;
- 1 536 ÷ 2 = 768 + 0;
- 768 ÷ 2 = 384 + 0;
- 384 ÷ 2 = 192 + 0;
- 192 ÷ 2 = 96 + 0;
- 96 ÷ 2 = 48 + 0;
- 48 ÷ 2 = 24 + 0;
- 24 ÷ 2 = 12 + 0;
- 12 ÷ 2 = 6 + 0;
- 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.
3 221 225 472(10) = 1100 0000 0000 0000 0000 0000 0000 0000(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 32.
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, 32,
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 3 221 225 472(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
3 221 225 472(10) = 0000 0000 0000 0000 0000 0000 0000 0000 1100 0000 0000 0000 0000 0000 0000 0000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.