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;
- 81 729 582 ÷ 2 = 40 864 791 + 0;
- 40 864 791 ÷ 2 = 20 432 395 + 1;
- 20 432 395 ÷ 2 = 10 216 197 + 1;
- 10 216 197 ÷ 2 = 5 108 098 + 1;
- 5 108 098 ÷ 2 = 2 554 049 + 0;
- 2 554 049 ÷ 2 = 1 277 024 + 1;
- 1 277 024 ÷ 2 = 638 512 + 0;
- 638 512 ÷ 2 = 319 256 + 0;
- 319 256 ÷ 2 = 159 628 + 0;
- 159 628 ÷ 2 = 79 814 + 0;
- 79 814 ÷ 2 = 39 907 + 0;
- 39 907 ÷ 2 = 19 953 + 1;
- 19 953 ÷ 2 = 9 976 + 1;
- 9 976 ÷ 2 = 4 988 + 0;
- 4 988 ÷ 2 = 2 494 + 0;
- 2 494 ÷ 2 = 1 247 + 0;
- 1 247 ÷ 2 = 623 + 1;
- 623 ÷ 2 = 311 + 1;
- 311 ÷ 2 = 155 + 1;
- 155 ÷ 2 = 77 + 1;
- 77 ÷ 2 = 38 + 1;
- 38 ÷ 2 = 19 + 0;
- 19 ÷ 2 = 9 + 1;
- 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.
81 729 582(10) = 100 1101 1111 0001 1000 0010 1110(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 27.
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, 27,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 32.
4. Get the positive binary computer representation on 32 bits (4 Bytes):
If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 32:
Number 81 729 582(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
81 729 582(10) = 0000 0100 1101 1111 0001 1000 0010 1110
Spaces were used to group digits: for binary, by 4, for decimal, by 3.