Final answer:
The formula to determine the maximum storage of a positive/negative number in two's complement involves subtracting 1 from the maximum positive number and calculating the two's complement for the maximum negative number.
Step-by-step explanation:
The formula to determine the maximum storage of a positive/negative number in two's complement is as follows:
- For a positive number, subtract 1 from the maximum positive number that can be represented in the given number of bits. This will give you the maximum positive number.
- For a negative number, calculate the two's complement of the maximum positive number. This can be done by inverting all the bits of the maximum positive number and then adding 1 to the result. The resulting number will be the maximum negative number that can be represented in the given number of bits.
For example, in an 8-bit system, the maximum positive number is 01111111 (127 in decimal). Therefore, the maximum negative number can be calculated as follows:
Inverting all the bits: 10000000
Adding 1 to the result: 10000001 (-127 in decimal).