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;
- 3 270 918 085 ÷ 2 = 1 635 459 042 + 1;
- 1 635 459 042 ÷ 2 = 817 729 521 + 0;
- 817 729 521 ÷ 2 = 408 864 760 + 1;
- 408 864 760 ÷ 2 = 204 432 380 + 0;
- 204 432 380 ÷ 2 = 102 216 190 + 0;
- 102 216 190 ÷ 2 = 51 108 095 + 0;
- 51 108 095 ÷ 2 = 25 554 047 + 1;
- 25 554 047 ÷ 2 = 12 777 023 + 1;
- 12 777 023 ÷ 2 = 6 388 511 + 1;
- 6 388 511 ÷ 2 = 3 194 255 + 1;
- 3 194 255 ÷ 2 = 1 597 127 + 1;
- 1 597 127 ÷ 2 = 798 563 + 1;
- 798 563 ÷ 2 = 399 281 + 1;
- 399 281 ÷ 2 = 199 640 + 1;
- 199 640 ÷ 2 = 99 820 + 0;
- 99 820 ÷ 2 = 49 910 + 0;
- 49 910 ÷ 2 = 24 955 + 0;
- 24 955 ÷ 2 = 12 477 + 1;
- 12 477 ÷ 2 = 6 238 + 1;
- 6 238 ÷ 2 = 3 119 + 0;
- 3 119 ÷ 2 = 1 559 + 1;
- 1 559 ÷ 2 = 779 + 1;
- 779 ÷ 2 = 389 + 1;
- 389 ÷ 2 = 194 + 1;
- 194 ÷ 2 = 97 + 0;
- 97 ÷ 2 = 48 + 1;
- 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.
3 270 918 085(10) = 1100 0010 1111 0110 0011 1111 1100 0101(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) 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, 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 3 270 918 085(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in two's complement representation:
3 270 918 085(10) = 0000 0000 0000 0000 0000 0000 0000 0000 1100 0010 1111 0110 0011 1111 1100 0101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.