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;
- 10 699 ÷ 2 = 5 349 + 1;
- 5 349 ÷ 2 = 2 674 + 1;
- 2 674 ÷ 2 = 1 337 + 0;
- 1 337 ÷ 2 = 668 + 1;
- 668 ÷ 2 = 334 + 0;
- 334 ÷ 2 = 167 + 0;
- 167 ÷ 2 = 83 + 1;
- 83 ÷ 2 = 41 + 1;
- 41 ÷ 2 = 20 + 1;
- 20 ÷ 2 = 10 + 0;
- 10 ÷ 2 = 5 + 0;
- 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.
10 699(10) = 10 1001 1100 1011(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 14.
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, 14,
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.
10 699(10) = 0010 1001 1100 1011
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.
-10 699(10) = !(0010 1001 1100 1011)
Number -10 699(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:
-10 699(10) = 1101 0110 0011 0100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.