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;
- 2 821 ÷ 2 = 1 410 + 1;
- 1 410 ÷ 2 = 705 + 0;
- 705 ÷ 2 = 352 + 1;
- 352 ÷ 2 = 176 + 0;
- 176 ÷ 2 = 88 + 0;
- 88 ÷ 2 = 44 + 0;
- 44 ÷ 2 = 22 + 0;
- 22 ÷ 2 = 11 + 0;
- 11 ÷ 2 = 5 + 1;
- 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.
2 821(10) = 1011 0000 0101(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 12.
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) indicates 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, 12,
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.
2 821(10) = 0000 1011 0000 0101
6. Get the negative integer number representation:
To write the negative integer number on 16 bits (2 Bytes),
as a signed binary in one's complement representation,
... replace all the bits on 0 with 1s and all the bits set on 1 with 0s.
Reverse the digits, flip the digits:
Replace the bits set on 0 with 1s and the bits set on 1 with 0s.
-2 821(10) = !(0000 1011 0000 0101)
Number -2 821(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in one's complement representation:
-2 821(10) = 1111 0100 1111 1010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.