Number of Hex digits needed to represent the 20-bit address of a memory location are______.
A
20
B
16
C
5
D
4

Question

Number of Hex digits needed to represent the 20-bit address of a memory location are______.

Examoogle · Accepted Answer

5

Explanation: To represent a binary address in hexadecimal, the binary bits are grouped into sets of four. Since each hexadecimal digit corresponds to exactly four binary digits (bits), a 20-bit address requires 20 divided by 4, which equals 5 hexadecimal digits.

Working Principle: The hexadecimal number system is base-16, where $16 = 2^4$. Because four binary bits are represented by a single hexadecimal digit (ranging from 0-F), any $n$-bit memory address can be converted to hexadecimal by dividing the total number of bits by 4. For a 20-bit address, the conversion is $\frac{20}{4} = 5$ hex digits.

Key Formulas: $	ext{Hex Digits} = \frac{N}{4}$ — where $N$ is the number of bits in the address

Key Points: Hexadecimal is a base-16 system.; Binary representation uses base-2 ($2^4 = 16$).; Each group of 4 binary bits maps uniquely to one hex character ($0-9, A-F$).; The 8085 microprocessor uses a 16-bit address (4 hex digits), while 8086 uses a 20-bit address (5 hex digits).

Advantages: Reduces the length of long binary strings significantly.; Easier for humans to read and write memory addresses.

Disadvantages: Requires conversion logic for hardware/software interaction.; Not directly understood by digital logic gates which operate on binary.

Applications: Memory addressing in microprocessors.; Representation of machine code and opcodes.; Debugging and system architecture documentation.

Additional Info: A 20-bit address space allows for $2^{20}$ locations, which is equivalent to 1 Megabyte of memory.. Option D (4) is incorrect as it only accounts for 16-bit addresses (e.g., 8085 processor).

Answer: C is correct — A 20-bit address requires 5 hexadecimal digits because each hex digit represents a 4-bit nibble.

Exam Tip: Remember that for any N-bit address, the number of hex digits is always ceil(N/4); this is a standard recurring question in exams like GATE and ISRO.

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