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;
- 27 012 077 ÷ 2 = 13 506 038 + 1;
- 13 506 038 ÷ 2 = 6 753 019 + 0;
- 6 753 019 ÷ 2 = 3 376 509 + 1;
- 3 376 509 ÷ 2 = 1 688 254 + 1;
- 1 688 254 ÷ 2 = 844 127 + 0;
- 844 127 ÷ 2 = 422 063 + 1;
- 422 063 ÷ 2 = 211 031 + 1;
- 211 031 ÷ 2 = 105 515 + 1;
- 105 515 ÷ 2 = 52 757 + 1;
- 52 757 ÷ 2 = 26 378 + 1;
- 26 378 ÷ 2 = 13 189 + 0;
- 13 189 ÷ 2 = 6 594 + 1;
- 6 594 ÷ 2 = 3 297 + 0;
- 3 297 ÷ 2 = 1 648 + 1;
- 1 648 ÷ 2 = 824 + 0;
- 824 ÷ 2 = 412 + 0;
- 412 ÷ 2 = 206 + 0;
- 206 ÷ 2 = 103 + 0;
- 103 ÷ 2 = 51 + 1;
- 51 ÷ 2 = 25 + 1;
- 25 ÷ 2 = 12 + 1;
- 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.
27 012 077(10) = 1 1001 1100 0010 1011 1110 1101(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 27 012 077(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
27 012 077(10) = 0000 0001 1001 1100 0010 1011 1110 1101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.