1. 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;
- 43 865 ÷ 2 = 21 932 + 1;
- 21 932 ÷ 2 = 10 966 + 0;
- 10 966 ÷ 2 = 5 483 + 0;
- 5 483 ÷ 2 = 2 741 + 1;
- 2 741 ÷ 2 = 1 370 + 1;
- 1 370 ÷ 2 = 685 + 0;
- 685 ÷ 2 = 342 + 1;
- 342 ÷ 2 = 171 + 0;
- 171 ÷ 2 = 85 + 1;
- 85 ÷ 2 = 42 + 1;
- 42 ÷ 2 = 21 + 0;
- 21 ÷ 2 = 10 + 1;
- 10 ÷ 2 = 5 + 0;
- 5 ÷ 2 = 2 + 1;
- 2 ÷ 2 = 1 + 0;
- 1 ÷ 2 = 0 + 1;
2. Construct the base 2 representation of the positive number:
Take all the remainders starting from the bottom of the list constructed above.
43 865(10) = 1010 1011 0101 1001(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 16.
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, 16,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 32.
4. 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:
Number 43 865(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
43 865(10) = 0000 0000 0000 0000 1010 1011 0101 1001
Spaces were used to group digits: for binary, by 4, for decimal, by 3.