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;
- 111 001 110 998 ÷ 2 = 55 500 555 499 + 0;
- 55 500 555 499 ÷ 2 = 27 750 277 749 + 1;
- 27 750 277 749 ÷ 2 = 13 875 138 874 + 1;
- 13 875 138 874 ÷ 2 = 6 937 569 437 + 0;
- 6 937 569 437 ÷ 2 = 3 468 784 718 + 1;
- 3 468 784 718 ÷ 2 = 1 734 392 359 + 0;
- 1 734 392 359 ÷ 2 = 867 196 179 + 1;
- 867 196 179 ÷ 2 = 433 598 089 + 1;
- 433 598 089 ÷ 2 = 216 799 044 + 1;
- 216 799 044 ÷ 2 = 108 399 522 + 0;
- 108 399 522 ÷ 2 = 54 199 761 + 0;
- 54 199 761 ÷ 2 = 27 099 880 + 1;
- 27 099 880 ÷ 2 = 13 549 940 + 0;
- 13 549 940 ÷ 2 = 6 774 970 + 0;
- 6 774 970 ÷ 2 = 3 387 485 + 0;
- 3 387 485 ÷ 2 = 1 693 742 + 1;
- 1 693 742 ÷ 2 = 846 871 + 0;
- 846 871 ÷ 2 = 423 435 + 1;
- 423 435 ÷ 2 = 211 717 + 1;
- 211 717 ÷ 2 = 105 858 + 1;
- 105 858 ÷ 2 = 52 929 + 0;
- 52 929 ÷ 2 = 26 464 + 1;
- 26 464 ÷ 2 = 13 232 + 0;
- 13 232 ÷ 2 = 6 616 + 0;
- 6 616 ÷ 2 = 3 308 + 0;
- 3 308 ÷ 2 = 1 654 + 0;
- 1 654 ÷ 2 = 827 + 0;
- 827 ÷ 2 = 413 + 1;
- 413 ÷ 2 = 206 + 1;
- 206 ÷ 2 = 103 + 0;
- 103 ÷ 2 = 51 + 1;
- 51 ÷ 2 = 25 + 1;
- 25 ÷ 2 = 12 + 1;
- 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.
111 001 110 998(10) = 1 1001 1101 1000 0010 1110 1000 1001 1101 0110(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 37.
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, 37,
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 111 001 110 998(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
111 001 110 998(10) = 0000 0000 0000 0000 0000 0000 0001 1001 1101 1000 0010 1110 1000 1001 1101 0110
Spaces were used to group digits: for binary, by 4, for decimal, by 3.