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;
- 3 109 ÷ 2 = 1 554 + 1;
- 1 554 ÷ 2 = 777 + 0;
- 777 ÷ 2 = 388 + 1;
- 388 ÷ 2 = 194 + 0;
- 194 ÷ 2 = 97 + 0;
- 97 ÷ 2 = 48 + 1;
- 48 ÷ 2 = 24 + 0;
- 24 ÷ 2 = 12 + 0;
- 12 ÷ 2 = 6 + 0;
- 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.
3 109(10) = 1100 0010 0101(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 12.
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, 12,
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:
3 109(10) = 0000 1100 0010 0101
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 -3 109(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-3 109(10) = 1000 1100 0010 0101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.