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;
- 10 110 010 937 ÷ 2 = 5 055 005 468 + 1;
- 5 055 005 468 ÷ 2 = 2 527 502 734 + 0;
- 2 527 502 734 ÷ 2 = 1 263 751 367 + 0;
- 1 263 751 367 ÷ 2 = 631 875 683 + 1;
- 631 875 683 ÷ 2 = 315 937 841 + 1;
- 315 937 841 ÷ 2 = 157 968 920 + 1;
- 157 968 920 ÷ 2 = 78 984 460 + 0;
- 78 984 460 ÷ 2 = 39 492 230 + 0;
- 39 492 230 ÷ 2 = 19 746 115 + 0;
- 19 746 115 ÷ 2 = 9 873 057 + 1;
- 9 873 057 ÷ 2 = 4 936 528 + 1;
- 4 936 528 ÷ 2 = 2 468 264 + 0;
- 2 468 264 ÷ 2 = 1 234 132 + 0;
- 1 234 132 ÷ 2 = 617 066 + 0;
- 617 066 ÷ 2 = 308 533 + 0;
- 308 533 ÷ 2 = 154 266 + 1;
- 154 266 ÷ 2 = 77 133 + 0;
- 77 133 ÷ 2 = 38 566 + 1;
- 38 566 ÷ 2 = 19 283 + 0;
- 19 283 ÷ 2 = 9 641 + 1;
- 9 641 ÷ 2 = 4 820 + 1;
- 4 820 ÷ 2 = 2 410 + 0;
- 2 410 ÷ 2 = 1 205 + 0;
- 1 205 ÷ 2 = 602 + 1;
- 602 ÷ 2 = 301 + 0;
- 301 ÷ 2 = 150 + 1;
- 150 ÷ 2 = 75 + 0;
- 75 ÷ 2 = 37 + 1;
- 37 ÷ 2 = 18 + 1;
- 18 ÷ 2 = 9 + 0;
- 9 ÷ 2 = 4 + 1;
- 4 ÷ 2 = 2 + 0;
- 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.
10 110 010 937(10) = 10 0101 1010 1001 1010 1000 0110 0011 1001(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) 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, 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 10 110 010 937(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
10 110 010 937(10) = 0000 0000 0000 0000 0000 0000 0000 0010 0101 1010 1001 1010 1000 0110 0011 1001
Spaces were used to group digits: for binary, by 4, for decimal, by 3.