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;
- 100 010 010 004 ÷ 2 = 50 005 005 002 + 0;
- 50 005 005 002 ÷ 2 = 25 002 502 501 + 0;
- 25 002 502 501 ÷ 2 = 12 501 251 250 + 1;
- 12 501 251 250 ÷ 2 = 6 250 625 625 + 0;
- 6 250 625 625 ÷ 2 = 3 125 312 812 + 1;
- 3 125 312 812 ÷ 2 = 1 562 656 406 + 0;
- 1 562 656 406 ÷ 2 = 781 328 203 + 0;
- 781 328 203 ÷ 2 = 390 664 101 + 1;
- 390 664 101 ÷ 2 = 195 332 050 + 1;
- 195 332 050 ÷ 2 = 97 666 025 + 0;
- 97 666 025 ÷ 2 = 48 833 012 + 1;
- 48 833 012 ÷ 2 = 24 416 506 + 0;
- 24 416 506 ÷ 2 = 12 208 253 + 0;
- 12 208 253 ÷ 2 = 6 104 126 + 1;
- 6 104 126 ÷ 2 = 3 052 063 + 0;
- 3 052 063 ÷ 2 = 1 526 031 + 1;
- 1 526 031 ÷ 2 = 763 015 + 1;
- 763 015 ÷ 2 = 381 507 + 1;
- 381 507 ÷ 2 = 190 753 + 1;
- 190 753 ÷ 2 = 95 376 + 1;
- 95 376 ÷ 2 = 47 688 + 0;
- 47 688 ÷ 2 = 23 844 + 0;
- 23 844 ÷ 2 = 11 922 + 0;
- 11 922 ÷ 2 = 5 961 + 0;
- 5 961 ÷ 2 = 2 980 + 1;
- 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.
100 010 010 004(10) = 1 0111 0100 1001 0000 1111 1010 0101 1001 0100(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 100 010 010 004(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:
100 010 010 004(10) = 0000 0000 0000 0000 0000 0000 0001 0111 0100 1001 0000 1111 1010 0101 1001 0100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.