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;
- 22 488 ÷ 2 = 11 244 + 0;
- 11 244 ÷ 2 = 5 622 + 0;
- 5 622 ÷ 2 = 2 811 + 0;
- 2 811 ÷ 2 = 1 405 + 1;
- 1 405 ÷ 2 = 702 + 1;
- 702 ÷ 2 = 351 + 0;
- 351 ÷ 2 = 175 + 1;
- 175 ÷ 2 = 87 + 1;
- 87 ÷ 2 = 43 + 1;
- 43 ÷ 2 = 21 + 1;
- 21 ÷ 2 = 10 + 1;
- 10 ÷ 2 = 5 + 0;
- 5 ÷ 2 = 2 + 1;
- 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.
22 488(10) = 101 0111 1101 1000(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 15.
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, 15,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 16.
5. Get the positive binary computer representation on 16 bits (2 Bytes):
If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 16:
22 488(10) = 0101 0111 1101 1000
6. Get the negative integer number representation:
To get the negative integer number representation on 16 bits (2 Bytes),
... change the first bit (the leftmost), from 0 to 1...
Number -22 488(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-22 488(10) = 1101 0111 1101 1000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.