Assertion (A) : Bit maps are not often used in memory management. Reason (R) :…

Free memory in a variable-partition (dynamic) allocation scheme can be tracked in more than one way. One method is a bit map: memory is divided into fixed-size allocation units, and each unit is represented by one bit -- 0 for free, 1 for allocated. To satisfy a request for k contiguous units, the memory manager must scan the bit map to locate a run of k consecutive 0 bits.

This scan is the operating cost of the bit-map method: its running time depends on how far the manager must search before finding a long-enough run of free bits, and in a fragmented map that search can extend across most of the table. Because of this scanning cost, operating systems more commonly track free memory with a linked list of holes (used with first-fit, best-fit, next-fit, or worst-fit placement), whose traversal cost is proportional to the number of holes rather than to the size of the whole map. This is exactly why bit maps see limited practical use for memory management -- because a run-length search over the bit map is comparatively slow.

Testing each of the four combinations against this cost analysis eliminates three of them:

• Keeping both statements true while treating the run-search cost as unrelated to the limited use would require some OTHER cause for the limited adoption -- nothing in the scanning-cost analysis above supports that.

• Treating the run-search claim as false would require that scanning a bit map for a free run is actually fast -- contradicted by the scanning-cost reasoning above.

• Treating the limited-use claim as false would require bit maps to be commonly used for memory management despite the scanning cost -- also contradicted above.

Both statements are therefore true, and the run-search cost is exactly the mechanism that explains the limited practical use of bit maps for memory management.