2. 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;
- 1 100 909 ÷ 2 = 550 454 + 1;
- 550 454 ÷ 2 = 275 227 + 0;
- 275 227 ÷ 2 = 137 613 + 1;
- 137 613 ÷ 2 = 68 806 + 1;
- 68 806 ÷ 2 = 34 403 + 0;
- 34 403 ÷ 2 = 17 201 + 1;
- 17 201 ÷ 2 = 8 600 + 1;
- 8 600 ÷ 2 = 4 300 + 0;
- 4 300 ÷ 2 = 2 150 + 0;
- 2 150 ÷ 2 = 1 075 + 0;
- 1 075 ÷ 2 = 537 + 1;
- 537 ÷ 2 = 268 + 1;
- 268 ÷ 2 = 134 + 0;
- 134 ÷ 2 = 67 + 0;
- 67 ÷ 2 = 33 + 1;
- 33 ÷ 2 = 16 + 1;
- 16 ÷ 2 = 8 + 0;
- 8 ÷ 2 = 4 + 0;
- 4 ÷ 2 = 2 + 0;
- 2 ÷ 2 = 1 + 0;
- 1 ÷ 2 = 0 + 1;
3. Construct the base 2 representation of the positive number:
Take all the remainders starting from the bottom of the list constructed above.
1 100 909(10) = 1 0000 1100 1100 0110 1101(2)
4. 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) 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, 21,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 32.
5. 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:
1 100 909(10) = 0000 0000 0001 0000 1100 1100 0110 1101
6. Get the negative integer number representation:
To get the negative integer number representation on 32 bits (4 Bytes),
... change the first bit (the leftmost), from 0 to 1...
Number -1 100 909(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-1 100 909(10) = 1000 0000 0001 0000 1100 1100 0110 1101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.