Perform the following operations involving eight-bit 2's complement numbers and indicate whether arithmetic overflow occurs. Check your answers by converting to decimal sign- and-magnitude representation. Correct any overflows encountered in problem 2 through sign extension and performing the addition again. Remember: Only in addition of two positive (two negative) numbers there could be an overflow. Remember: No overflow can happen if you add a positive number with a negative number.

An argument is said to be valid when its conclusion follows logically from its premises. In other words, if the premises are true, then the conclusion must also be true.

On the other hand, an argument is said to be invalid when its conclusion does not follow logically from its premises. This means that even if the premises are true, the conclusion may not necessarily be true.
For example, consider the following argument:
Premise 1: All cats have tails.
Premise 2: Tom is a cat.
Conclusion: Therefore, Tom has a tail.
This argument is valid because if we accept the premises as true, then the conclusion logically follows. However, consider the following argument:
Premise 1: All dogs have tails.
Premise 2: Tom is a cat.
Conclusion: Therefore, Tom has a tail.
This argument is invalid because even though the premises may be true, the conclusion does not logically follow from them. In this case, the fact that all dogs have tails does not necessarily mean that all cats have tails, so we cannot use this premise to support the conclusion.
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To calculate the maximum torsional shear stress (τmax) in a solid circular shaft, we can use the following formula:

τmax = (16 * T) / (π * d^3)

Where:T is the torque being transmitted (in lb·in or lb·ft),

d is the diameter of the shaft (in inches).

First, let's convert the power of 125 hp to torque (T) in lb·ft. We can use the following equatio

T = (P * 5252) / NWhere:

P is the power in horsepower (hp),

N is the rotational speed in revolutions per minute (rpm).Converting 125 hp to torque

T = (125 * 5252) / 525 = 125 lbNow we can calculate the maximum torsional shear stress

τmax = (16 * 125) / (π * (1.25/2)^3)τmax = (16 * 125) / (π * (0.625)^3

τmax = (16 * 125) / (π * 0.24414)τmax = 8000 / 0.76793τmax ≈ 10408.84 psi (rounded to two decimal places)

Therefore, the maximum torsional shear stress in the solid circular shaft is approximately 10408.84 psi.

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In C programming, the expression "&(&i)" is not considered valid.

Here's a step-by-step explanation:
1. "i" represents a variable, which can store an integer value. To declare a variable "i" as an integer, you would write "int i;".
2. "&i" refers to the memory address of the variable "i". The ampersand (&) is known as the "address-of" operator, and it is used to get the address of a variable in memory.
3. Now, let's consider "&(&i)": this expression attempts to get the address of the address of the variable "i". However, this is not valid in C, because the "address-of" operator cannot be applied to the result of another "address-of" operator.
In summary, the expression "&(&i)" is not valid in C programming, as you cannot use the "address-of" operator on the result of another "address-of" operator.

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