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;
- 11 110 999 970 ÷ 2 = 5 555 499 985 + 0;
- 5 555 499 985 ÷ 2 = 2 777 749 992 + 1;
- 2 777 749 992 ÷ 2 = 1 388 874 996 + 0;
- 1 388 874 996 ÷ 2 = 694 437 498 + 0;
- 694 437 498 ÷ 2 = 347 218 749 + 0;
- 347 218 749 ÷ 2 = 173 609 374 + 1;
- 173 609 374 ÷ 2 = 86 804 687 + 0;
- 86 804 687 ÷ 2 = 43 402 343 + 1;
- 43 402 343 ÷ 2 = 21 701 171 + 1;
- 21 701 171 ÷ 2 = 10 850 585 + 1;
- 10 850 585 ÷ 2 = 5 425 292 + 1;
- 5 425 292 ÷ 2 = 2 712 646 + 0;
- 2 712 646 ÷ 2 = 1 356 323 + 0;
- 1 356 323 ÷ 2 = 678 161 + 1;
- 678 161 ÷ 2 = 339 080 + 1;
- 339 080 ÷ 2 = 169 540 + 0;
- 169 540 ÷ 2 = 84 770 + 0;
- 84 770 ÷ 2 = 42 385 + 0;
- 42 385 ÷ 2 = 21 192 + 1;
- 21 192 ÷ 2 = 10 596 + 0;
- 10 596 ÷ 2 = 5 298 + 0;
- 5 298 ÷ 2 = 2 649 + 0;
- 2 649 ÷ 2 = 1 324 + 1;
- 1 324 ÷ 2 = 662 + 0;
- 662 ÷ 2 = 331 + 0;
- 331 ÷ 2 = 165 + 1;
- 165 ÷ 2 = 82 + 1;
- 82 ÷ 2 = 41 + 0;
- 41 ÷ 2 = 20 + 1;
- 20 ÷ 2 = 10 + 0;
- 10 ÷ 2 = 5 + 0;
- 5 ÷ 2 = 2 + 1;
- 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.
11 110 999 970(10) = 10 1001 0110 0100 0100 0110 0111 1010 0010(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) 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, 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 11 110 999 970(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:
11 110 999 970(10) = 0000 0000 0000 0000 0000 0000 0000 0010 1001 0110 0100 0100 0110 0111 1010 0010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.