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;
- 26 041 975 ÷ 2 = 13 020 987 + 1;
- 13 020 987 ÷ 2 = 6 510 493 + 1;
- 6 510 493 ÷ 2 = 3 255 246 + 1;
- 3 255 246 ÷ 2 = 1 627 623 + 0;
- 1 627 623 ÷ 2 = 813 811 + 1;
- 813 811 ÷ 2 = 406 905 + 1;
- 406 905 ÷ 2 = 203 452 + 1;
- 203 452 ÷ 2 = 101 726 + 0;
- 101 726 ÷ 2 = 50 863 + 0;
- 50 863 ÷ 2 = 25 431 + 1;
- 25 431 ÷ 2 = 12 715 + 1;
- 12 715 ÷ 2 = 6 357 + 1;
- 6 357 ÷ 2 = 3 178 + 1;
- 3 178 ÷ 2 = 1 589 + 0;
- 1 589 ÷ 2 = 794 + 1;
- 794 ÷ 2 = 397 + 0;
- 397 ÷ 2 = 198 + 1;
- 198 ÷ 2 = 99 + 0;
- 99 ÷ 2 = 49 + 1;
- 49 ÷ 2 = 24 + 1;
- 24 ÷ 2 = 12 + 0;
- 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.
26 041 975(10) = 1 1000 1101 0101 1110 0111 0111(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 25.
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, 25,
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 26 041 975(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
26 041 975(10) = 0000 0001 1000 1101 0101 1110 0111 0111
Spaces were used to group digits: for binary, by 4, for decimal, by 3.