True or false, and why: the memory data register and the memory address register will likely have the same number of bits.
A memory address register, MAR, stores the address that the CPU is interested in. If MAR is k-bit wide then the system is said to be k-bit addressable (or has k-bit addresses). Most modern system are 32-bit or 64-bit addressable.
Memory data register or MDR holds the value returned by the memory system. If MDR is n-bit wide, then the system can deal with (at the maximum) n-bits.
So, while the MDR has the same size as the memory location and an addressability of a memory as 64-bits will mean 64-bit MDR; the size of MAR is determined by number of locations and will thus likely be different.
so the difference in the number of bits is due to differences between size of memory location and number of locations.