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;
- 1 210 287 ÷ 2 = 605 143 + 1;
- 605 143 ÷ 2 = 302 571 + 1;
- 302 571 ÷ 2 = 151 285 + 1;
- 151 285 ÷ 2 = 75 642 + 1;
- 75 642 ÷ 2 = 37 821 + 0;
- 37 821 ÷ 2 = 18 910 + 1;
- 18 910 ÷ 2 = 9 455 + 0;
- 9 455 ÷ 2 = 4 727 + 1;
- 4 727 ÷ 2 = 2 363 + 1;
- 2 363 ÷ 2 = 1 181 + 1;
- 1 181 ÷ 2 = 590 + 1;
- 590 ÷ 2 = 295 + 0;
- 295 ÷ 2 = 147 + 1;
- 147 ÷ 2 = 73 + 1;
- 73 ÷ 2 = 36 + 1;
- 36 ÷ 2 = 18 + 0;
- 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.
1 210 287(10) = 1 0010 0111 0111 1010 1111(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 21.
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, 21,
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 1 210 287(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:
1 210 287(10) = 0000 0000 0001 0010 0111 0111 1010 1111
Spaces were used to group digits: for binary, by 4, for decimal, by 3.