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;
- 6 867 ÷ 2 = 3 433 + 1;
- 3 433 ÷ 2 = 1 716 + 1;
- 1 716 ÷ 2 = 858 + 0;
- 858 ÷ 2 = 429 + 0;
- 429 ÷ 2 = 214 + 1;
- 214 ÷ 2 = 107 + 0;
- 107 ÷ 2 = 53 + 1;
- 53 ÷ 2 = 26 + 1;
- 26 ÷ 2 = 13 + 0;
- 13 ÷ 2 = 6 + 1;
- 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.
6 867(10) = 1 1010 1101 0011(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 13.
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, 13,
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:
6 867(10) = 0001 1010 1101 0011
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 -6 867(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-6 867(10) = 1001 1010 1101 0011
Spaces were used to group digits: for binary, by 4, for decimal, by 3.