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;
- 100 001 011 009 ÷ 2 = 50 000 505 504 + 1;
- 50 000 505 504 ÷ 2 = 25 000 252 752 + 0;
- 25 000 252 752 ÷ 2 = 12 500 126 376 + 0;
- 12 500 126 376 ÷ 2 = 6 250 063 188 + 0;
- 6 250 063 188 ÷ 2 = 3 125 031 594 + 0;
- 3 125 031 594 ÷ 2 = 1 562 515 797 + 0;
- 1 562 515 797 ÷ 2 = 781 257 898 + 1;
- 781 257 898 ÷ 2 = 390 628 949 + 0;
- 390 628 949 ÷ 2 = 195 314 474 + 1;
- 195 314 474 ÷ 2 = 97 657 237 + 0;
- 97 657 237 ÷ 2 = 48 828 618 + 1;
- 48 828 618 ÷ 2 = 24 414 309 + 0;
- 24 414 309 ÷ 2 = 12 207 154 + 1;
- 12 207 154 ÷ 2 = 6 103 577 + 0;
- 6 103 577 ÷ 2 = 3 051 788 + 1;
- 3 051 788 ÷ 2 = 1 525 894 + 0;
- 1 525 894 ÷ 2 = 762 947 + 0;
- 762 947 ÷ 2 = 381 473 + 1;
- 381 473 ÷ 2 = 190 736 + 1;
- 190 736 ÷ 2 = 95 368 + 0;
- 95 368 ÷ 2 = 47 684 + 0;
- 47 684 ÷ 2 = 23 842 + 0;
- 23 842 ÷ 2 = 11 921 + 0;
- 11 921 ÷ 2 = 5 960 + 1;
- 5 960 ÷ 2 = 2 980 + 0;
- 2 980 ÷ 2 = 1 490 + 0;
- 1 490 ÷ 2 = 745 + 0;
- 745 ÷ 2 = 372 + 1;
- 372 ÷ 2 = 186 + 0;
- 186 ÷ 2 = 93 + 0;
- 93 ÷ 2 = 46 + 1;
- 46 ÷ 2 = 23 + 0;
- 23 ÷ 2 = 11 + 1;
- 11 ÷ 2 = 5 + 1;
- 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.
100 001 011 009(10) = 1 0111 0100 1000 1000 0110 0101 0101 0100 0001(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) 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, 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 100 001 011 009(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:
100 001 011 009(10) = 0000 0000 0000 0000 0000 0000 0001 0111 0100 1000 1000 0110 0101 0101 0100 0001
Spaces were used to group digits: for binary, by 4, for decimal, by 3.