An embedded computer uses 8-bit 2's complement representation for signed integers. What is the minimum negative integer value which can be represented in this computer?
Explanation
In digital computer systems, 2's complement is the standard method used to represent signed integers. For a system using n bits, the range of representable integers is determined by specific formulas.
1. Formula for the Range
For an n-bit number in 2's complement representation, the range of values is given by:
Minimum Value: −2n−1
Maximum Value: 2n−1−1
2. Calculation
In the problem provided in image_c4b7a0.png, the computer uses an 8-bit representation. Therefore, we set n=8.
To find the minimum negative integer, we use the formula:
Minimum Value=−28−1
Minimum Value=−27
Minimum Value=−128
Conversely, the maximum positive integer that can be represented is 28−1−1, which is 27−1=127.
Conclusion
The minimum negative integer value that can be represented by an 8-bit 2's complement system is −128.
Correct Option: 3 (-128)
