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;
- 8 612 717 365 ÷ 2 = 4 306 358 682 + 1;
- 4 306 358 682 ÷ 2 = 2 153 179 341 + 0;
- 2 153 179 341 ÷ 2 = 1 076 589 670 + 1;
- 1 076 589 670 ÷ 2 = 538 294 835 + 0;
- 538 294 835 ÷ 2 = 269 147 417 + 1;
- 269 147 417 ÷ 2 = 134 573 708 + 1;
- 134 573 708 ÷ 2 = 67 286 854 + 0;
- 67 286 854 ÷ 2 = 33 643 427 + 0;
- 33 643 427 ÷ 2 = 16 821 713 + 1;
- 16 821 713 ÷ 2 = 8 410 856 + 1;
- 8 410 856 ÷ 2 = 4 205 428 + 0;
- 4 205 428 ÷ 2 = 2 102 714 + 0;
- 2 102 714 ÷ 2 = 1 051 357 + 0;
- 1 051 357 ÷ 2 = 525 678 + 1;
- 525 678 ÷ 2 = 262 839 + 0;
- 262 839 ÷ 2 = 131 419 + 1;
- 131 419 ÷ 2 = 65 709 + 1;
- 65 709 ÷ 2 = 32 854 + 1;
- 32 854 ÷ 2 = 16 427 + 0;
- 16 427 ÷ 2 = 8 213 + 1;
- 8 213 ÷ 2 = 4 106 + 1;
- 4 106 ÷ 2 = 2 053 + 0;
- 2 053 ÷ 2 = 1 026 + 1;
- 1 026 ÷ 2 = 513 + 0;
- 513 ÷ 2 = 256 + 1;
- 256 ÷ 2 = 128 + 0;
- 128 ÷ 2 = 64 + 0;
- 64 ÷ 2 = 32 + 0;
- 32 ÷ 2 = 16 + 0;
- 16 ÷ 2 = 8 + 0;
- 8 ÷ 2 = 4 + 0;
- 4 ÷ 2 = 2 + 0;
- 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.
8 612 717 365(10) = 10 0000 0001 0101 1011 1010 0011 0011 0101(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 8 612 717 365(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
8 612 717 365(10) = 0000 0000 0000 0000 0000 0000 0000 0010 0000 0001 0101 1011 1010 0011 0011 0101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.