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;
- 666 680 ÷ 2 = 333 340 + 0;
- 333 340 ÷ 2 = 166 670 + 0;
- 166 670 ÷ 2 = 83 335 + 0;
- 83 335 ÷ 2 = 41 667 + 1;
- 41 667 ÷ 2 = 20 833 + 1;
- 20 833 ÷ 2 = 10 416 + 1;
- 10 416 ÷ 2 = 5 208 + 0;
- 5 208 ÷ 2 = 2 604 + 0;
- 2 604 ÷ 2 = 1 302 + 0;
- 1 302 ÷ 2 = 651 + 0;
- 651 ÷ 2 = 325 + 1;
- 325 ÷ 2 = 162 + 1;
- 162 ÷ 2 = 81 + 0;
- 81 ÷ 2 = 40 + 1;
- 40 ÷ 2 = 20 + 0;
- 20 ÷ 2 = 10 + 0;
- 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.
666 680(10) = 1010 0010 1100 0011 1000(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 20.
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, 20,
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:
666 680(10) = 0000 0000 0000 1010 0010 1100 0011 1000
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 -666 680(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-666 680(10) = 1000 0000 0000 1010 0010 1100 0011 1000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.