At a particular time of computation, the value of counting...

At a particular time of computation, the value of counting semaphore is 7 . Then 20 wait operations and ' $x$ 'signal operations were completed on this semaphore. If the final value of the semaphore is 5 , what is $x$ ?
(A) 18
(B) 13
(C) 5
(D) 0

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Key Concepts

Signal Operation

The signal operation, also referred to as V or up, is an atomic action that increments the semaphore's count. This increment may allow blocked processes to resume execution as it indicates that a resource has been released.

Semaphore Arithmetic

Semaphore arithmetic involves computing the current value of a semaphore by adjusting its initial value based on the number of wait and signal operations performed. By subtracting the number of waits and adding the number of signals from the initial count, one can determine the semaphore's final state.

Counting Semaphore

A counting semaphore is a synchronization tool used in concurrent programming to manage access to a finite number of resources. It maintains a counter that represents the number of available resources, allowing processes to proceed if the counter is positive and to block if the counter is zero or less.

Wait Operation

The wait operation, often symbolized as P or down, is an atomic action that decrements the semaphore's count. If decrementing causes the count to drop below zero, the process executing the operation may be blocked until sufficient resources are released.

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