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;
- 230 353 ÷ 2 = 115 176 + 1;
- 115 176 ÷ 2 = 57 588 + 0;
- 57 588 ÷ 2 = 28 794 + 0;
- 28 794 ÷ 2 = 14 397 + 0;
- 14 397 ÷ 2 = 7 198 + 1;
- 7 198 ÷ 2 = 3 599 + 0;
- 3 599 ÷ 2 = 1 799 + 1;
- 1 799 ÷ 2 = 899 + 1;
- 899 ÷ 2 = 449 + 1;
- 449 ÷ 2 = 224 + 1;
- 224 ÷ 2 = 112 + 0;
- 112 ÷ 2 = 56 + 0;
- 56 ÷ 2 = 28 + 0;
- 28 ÷ 2 = 14 + 0;
- 14 ÷ 2 = 7 + 0;
- 7 ÷ 2 = 3 + 1;
- 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.
230 353(10) = 11 1000 0011 1101 0001(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 18.
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, 18,
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:
230 353(10) = 0000 0000 0000 0011 1000 0011 1101 0001
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 -230 353(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-230 353(10) = 1000 0000 0000 0011 1000 0011 1101 0001
Spaces were used to group digits: for binary, by 4, for decimal, by 3.