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;
- 111 001 100 111 059 ÷ 2 = 55 500 550 055 529 + 1;
- 55 500 550 055 529 ÷ 2 = 27 750 275 027 764 + 1;
- 27 750 275 027 764 ÷ 2 = 13 875 137 513 882 + 0;
- 13 875 137 513 882 ÷ 2 = 6 937 568 756 941 + 0;
- 6 937 568 756 941 ÷ 2 = 3 468 784 378 470 + 1;
- 3 468 784 378 470 ÷ 2 = 1 734 392 189 235 + 0;
- 1 734 392 189 235 ÷ 2 = 867 196 094 617 + 1;
- 867 196 094 617 ÷ 2 = 433 598 047 308 + 1;
- 433 598 047 308 ÷ 2 = 216 799 023 654 + 0;
- 216 799 023 654 ÷ 2 = 108 399 511 827 + 0;
- 108 399 511 827 ÷ 2 = 54 199 755 913 + 1;
- 54 199 755 913 ÷ 2 = 27 099 877 956 + 1;
- 27 099 877 956 ÷ 2 = 13 549 938 978 + 0;
- 13 549 938 978 ÷ 2 = 6 774 969 489 + 0;
- 6 774 969 489 ÷ 2 = 3 387 484 744 + 1;
- 3 387 484 744 ÷ 2 = 1 693 742 372 + 0;
- 1 693 742 372 ÷ 2 = 846 871 186 + 0;
- 846 871 186 ÷ 2 = 423 435 593 + 0;
- 423 435 593 ÷ 2 = 211 717 796 + 1;
- 211 717 796 ÷ 2 = 105 858 898 + 0;
- 105 858 898 ÷ 2 = 52 929 449 + 0;
- 52 929 449 ÷ 2 = 26 464 724 + 1;
- 26 464 724 ÷ 2 = 13 232 362 + 0;
- 13 232 362 ÷ 2 = 6 616 181 + 0;
- 6 616 181 ÷ 2 = 3 308 090 + 1;
- 3 308 090 ÷ 2 = 1 654 045 + 0;
- 1 654 045 ÷ 2 = 827 022 + 1;
- 827 022 ÷ 2 = 413 511 + 0;
- 413 511 ÷ 2 = 206 755 + 1;
- 206 755 ÷ 2 = 103 377 + 1;
- 103 377 ÷ 2 = 51 688 + 1;
- 51 688 ÷ 2 = 25 844 + 0;
- 25 844 ÷ 2 = 12 922 + 0;
- 12 922 ÷ 2 = 6 461 + 0;
- 6 461 ÷ 2 = 3 230 + 1;
- 3 230 ÷ 2 = 1 615 + 0;
- 1 615 ÷ 2 = 807 + 1;
- 807 ÷ 2 = 403 + 1;
- 403 ÷ 2 = 201 + 1;
- 201 ÷ 2 = 100 + 1;
- 100 ÷ 2 = 50 + 0;
- 50 ÷ 2 = 25 + 0;
- 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.
111 001 100 111 059(10) = 110 0100 1111 0100 0111 0101 0010 0100 0100 1100 1101 0011(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 47.
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, 47,
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 111 001 100 111 059(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:
Spaces were used to group digits: for binary, by 4, for decimal, by 3.