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;
- 222 415 ÷ 2 = 111 207 + 1;
- 111 207 ÷ 2 = 55 603 + 1;
- 55 603 ÷ 2 = 27 801 + 1;
- 27 801 ÷ 2 = 13 900 + 1;
- 13 900 ÷ 2 = 6 950 + 0;
- 6 950 ÷ 2 = 3 475 + 0;
- 3 475 ÷ 2 = 1 737 + 1;
- 1 737 ÷ 2 = 868 + 1;
- 868 ÷ 2 = 434 + 0;
- 434 ÷ 2 = 217 + 0;
- 217 ÷ 2 = 108 + 1;
- 108 ÷ 2 = 54 + 0;
- 54 ÷ 2 = 27 + 0;
- 27 ÷ 2 = 13 + 1;
- 13 ÷ 2 = 6 + 1;
- 6 ÷ 2 = 3 + 0;
- 3 ÷ 2 = 1 + 1;
- 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.
222 415(10) = 11 0110 0100 1100 1111(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 18.
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, 18,
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:
222 415(10) = 0000 0000 0000 0011 0110 0100 1100 1111
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 -222 415(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-222 415(10) = 1000 0000 0000 0011 0110 0100 1100 1111
Spaces were used to group digits: for binary, by 4, for decimal, by 3.