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;
- 7 186 ÷ 2 = 3 593 + 0;
- 3 593 ÷ 2 = 1 796 + 1;
- 1 796 ÷ 2 = 898 + 0;
- 898 ÷ 2 = 449 + 0;
- 449 ÷ 2 = 224 + 1;
- 224 ÷ 2 = 112 + 0;
- 112 ÷ 2 = 56 + 0;
- 56 ÷ 2 = 28 + 0;
- 28 ÷ 2 = 14 + 0;
- 14 ÷ 2 = 7 + 0;
- 7 ÷ 2 = 3 + 1;
- 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.
7 186(10) = 1 1100 0001 0010(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) 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, 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.
7 186(10) = 0001 1100 0001 0010
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.
-7 186(10) = !(0001 1100 0001 0010)
Number -7 186(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:
-7 186(10) = 1110 0011 1110 1101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.