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;
- 7 998 046 888 ÷ 2 = 3 999 023 444 + 0;
- 3 999 023 444 ÷ 2 = 1 999 511 722 + 0;
- 1 999 511 722 ÷ 2 = 999 755 861 + 0;
- 999 755 861 ÷ 2 = 499 877 930 + 1;
- 499 877 930 ÷ 2 = 249 938 965 + 0;
- 249 938 965 ÷ 2 = 124 969 482 + 1;
- 124 969 482 ÷ 2 = 62 484 741 + 0;
- 62 484 741 ÷ 2 = 31 242 370 + 1;
- 31 242 370 ÷ 2 = 15 621 185 + 0;
- 15 621 185 ÷ 2 = 7 810 592 + 1;
- 7 810 592 ÷ 2 = 3 905 296 + 0;
- 3 905 296 ÷ 2 = 1 952 648 + 0;
- 1 952 648 ÷ 2 = 976 324 + 0;
- 976 324 ÷ 2 = 488 162 + 0;
- 488 162 ÷ 2 = 244 081 + 0;
- 244 081 ÷ 2 = 122 040 + 1;
- 122 040 ÷ 2 = 61 020 + 0;
- 61 020 ÷ 2 = 30 510 + 0;
- 30 510 ÷ 2 = 15 255 + 0;
- 15 255 ÷ 2 = 7 627 + 1;
- 7 627 ÷ 2 = 3 813 + 1;
- 3 813 ÷ 2 = 1 906 + 1;
- 1 906 ÷ 2 = 953 + 0;
- 953 ÷ 2 = 476 + 1;
- 476 ÷ 2 = 238 + 0;
- 238 ÷ 2 = 119 + 0;
- 119 ÷ 2 = 59 + 1;
- 59 ÷ 2 = 29 + 1;
- 29 ÷ 2 = 14 + 1;
- 14 ÷ 2 = 7 + 0;
- 7 ÷ 2 = 3 + 1;
- 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.
7 998 046 888(10) = 1 1101 1100 1011 1000 1000 0010 1010 1000(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 7 998 046 888(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:
7 998 046 888(10) = 0000 0000 0000 0000 0000 0000 0000 0001 1101 1100 1011 1000 1000 0010 1010 1000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.