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;
- 1 699 ÷ 2 = 849 + 1;
- 849 ÷ 2 = 424 + 1;
- 424 ÷ 2 = 212 + 0;
- 212 ÷ 2 = 106 + 0;
- 106 ÷ 2 = 53 + 0;
- 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.
1 699(10) = 110 1010 0011(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 11.
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, 11,
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.
1 699(10) = 0000 0110 1010 0011
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.
-1 699(10) = !(0000 0110 1010 0011)
Number -1 699(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:
-1 699(10) = 1111 1001 0101 1100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.