If memory address is of 4-bits, then total no. of word in memory are_____.

Question

Examoogle · Accepted Answer

16

Explanation: The number of memory words (also known as memory locations) is determined by the total number of unique addresses that can be generated by the memory address bus. If the address bus is $n$ bits wide, it can uniquely identify $2^n$ distinct memory locations.

Working Principle: In a digital system, each memory location is assigned a unique binary address. A binary number of $n$ bits allows for $2^n$ combinations of 0s and 1s, where each combination acts as a pointer to a specific memory word. For a 4-bit address, the range of addresses spans from $0000_2$ to $1111_2$, which corresponds to decimal 0 through 15, resulting in exactly 16 total locations.

Key Formulas: $N = 2^n$ — where $N$ is the number of words and $n$ is the number of address bits

Key Points: The address bus width directly defines the address space of the processor.; Increasing the address bus by 1 bit doubles the total memory capacity.; A 4-bit address space is very small, typical of early 4-bit microprocessors like the Intel 4004.

Advantages: Direct mapping of unique binary codes to hardware storage registers.; Predictable memory architecture based on power-of-two growth.

Disadvantages: Exponential growth of address lines needed to support large memory sizes.; Hardware complexity increases as the bit-width of the address decoder expands.

Applications: Small embedded systems; Digital register file addressing; Instruction pointer indexing

Additional Info: A 4-bit address register can hold values from $0000$ to $1111$.. Option A (4) corresponds to $2^2$, Option B (64) corresponds to $2^6$, and Option D (8) corresponds to $2^3$.

Answer: C is correct — a 4-bit address line allows for $2^4 = 16$ unique binary addresses, which corresponds to 16 distinct memory words.

Exam Tip: Remember that for any memory-related exam question, capacity is always $2^n$ where $n$ is the number of bits in the address bus.

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