. Suppose that we want to add eight n-bit signed (two's complement) numbers. How many bits are needed for the sum so that no overflow will occur.
explain and provide a full solution.
Introduction:
n digital systems, adding signed numbers is a common operation, especially in computer arithmetic. When adding signed numbers in two's complement representation, overflow can occur if the result is too large (positive) or too small (negative) to be represented using a fixed number of bits. Overflow can result in errors and unexpected behavior, so it's important to ensure that enough bits are allocated to the result of the addition to prevent overflow.
The number of bits required for the sum depends on the number of input values and their bit representation. In this context, we are asked to determine the number of bits needed to add eight signed n-bit two's complement numbers without overflow.
The approach can be followed to determine the minimum number of bits needed to represent the sum without overflow. This calculation provides a useful guideline for designing digital systems that perform the addition of signed numbers.
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