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;
- 83 539 ÷ 2 = 41 769 + 1;
- 41 769 ÷ 2 = 20 884 + 1;
- 20 884 ÷ 2 = 10 442 + 0;
- 10 442 ÷ 2 = 5 221 + 0;
- 5 221 ÷ 2 = 2 610 + 1;
- 2 610 ÷ 2 = 1 305 + 0;
- 1 305 ÷ 2 = 652 + 1;
- 652 ÷ 2 = 326 + 0;
- 326 ÷ 2 = 163 + 0;
- 163 ÷ 2 = 81 + 1;
- 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.
83 539(10) = 1 0100 0110 0101 0011(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 17.
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, 17,
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:
83 539(10) = 0000 0000 0000 0001 0100 0110 0101 0011
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 -83 539(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-83 539(10) = 1000 0000 0000 0001 0100 0110 0101 0011
Spaces were used to group digits: for binary, by 4, for decimal, by 3.