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;
- 19 780 ÷ 2 = 9 890 + 0;
- 9 890 ÷ 2 = 4 945 + 0;
- 4 945 ÷ 2 = 2 472 + 1;
- 2 472 ÷ 2 = 1 236 + 0;
- 1 236 ÷ 2 = 618 + 0;
- 618 ÷ 2 = 309 + 0;
- 309 ÷ 2 = 154 + 1;
- 154 ÷ 2 = 77 + 0;
- 77 ÷ 2 = 38 + 1;
- 38 ÷ 2 = 19 + 0;
- 19 ÷ 2 = 9 + 1;
- 9 ÷ 2 = 4 + 1;
- 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.
19 780(10) = 100 1101 0100 0100(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:
19 780(10) = 0100 1101 0100 0100
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 -19 780(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-19 780(10) = 1100 1101 0100 0100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.