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;
- 6 552 442 618 ÷ 2 = 3 276 221 309 + 0;
- 3 276 221 309 ÷ 2 = 1 638 110 654 + 1;
- 1 638 110 654 ÷ 2 = 819 055 327 + 0;
- 819 055 327 ÷ 2 = 409 527 663 + 1;
- 409 527 663 ÷ 2 = 204 763 831 + 1;
- 204 763 831 ÷ 2 = 102 381 915 + 1;
- 102 381 915 ÷ 2 = 51 190 957 + 1;
- 51 190 957 ÷ 2 = 25 595 478 + 1;
- 25 595 478 ÷ 2 = 12 797 739 + 0;
- 12 797 739 ÷ 2 = 6 398 869 + 1;
- 6 398 869 ÷ 2 = 3 199 434 + 1;
- 3 199 434 ÷ 2 = 1 599 717 + 0;
- 1 599 717 ÷ 2 = 799 858 + 1;
- 799 858 ÷ 2 = 399 929 + 0;
- 399 929 ÷ 2 = 199 964 + 1;
- 199 964 ÷ 2 = 99 982 + 0;
- 99 982 ÷ 2 = 49 991 + 0;
- 49 991 ÷ 2 = 24 995 + 1;
- 24 995 ÷ 2 = 12 497 + 1;
- 12 497 ÷ 2 = 6 248 + 1;
- 6 248 ÷ 2 = 3 124 + 0;
- 3 124 ÷ 2 = 1 562 + 0;
- 1 562 ÷ 2 = 781 + 0;
- 781 ÷ 2 = 390 + 1;
- 390 ÷ 2 = 195 + 0;
- 195 ÷ 2 = 97 + 1;
- 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.
6 552 442 618(10) = 1 1000 0110 1000 1110 0101 0110 1111 1010(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 33.
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, 33,
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 6 552 442 618(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in one's complement representation:
6 552 442 618(10) = 0000 0000 0000 0000 0000 0000 0000 0001 1000 0110 1000 1110 0101 0110 1111 1010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.