Question

The main advantage of hexadecimal number is the ease of conversion from hexadecimal to....... and vice versa.

• A. Decimal
• B. binary
• C. ASCII
• D. BCD

Hint:

Hexadecimal is effectively just a shorthand representation for binary; one hex digit compresses exactly four binary bits, drastically reducing the length of strings representing memory addresses and data.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question tests the fundamental reason why the hexadecimal number system is so widely utilized in computer science alongside binary.


Step 2: Detailed Explanation:
Hexadecimal is a base-16 number system, while binary is a base-2 number system.
Since \( 16 = 2^4 \), each individual hexadecimal digit perfectly corresponds to a distinct 4-bit binary sequence, also known as a nibble.
This direct bit-level mapping means that converting between hexadecimal and binary is a simple, direct substitution process without complex mathematical operations.
Converting to decimal, on the other hand, requires polynomial evaluation and repeated division, which is computationally heavier.
Therefore, the main advantage of hexadecimal representation is the ease of conversion to and from binary, making it a compact way for humans to read long binary machine codes.


Step 3: Final Answer:
The correct choice is binary.

Answer 2

This question asks why the hexadecimal number system is considered convenient for representing computer data compared to other systems. Let's examine each option by testing whether it actually offers a simple, direct conversion process with hexadecimal.

1. Decimal: Converting hexadecimal to decimal requires evaluating each digit as a power of 16 and summing the results, for example \( (2F)_{16} = 2 \times 16^1 + 15 \times 16^0 \). This involves genuine arithmetic with powers of 16, which is slow to do by hand and offers no shortcut, so decimal is not the system hexadecimal converts to easily.
2. Binary: Since \( 16 = 2^4 \), every single hexadecimal digit corresponds exactly to a 4-bit binary group. Conversion in either direction is a direct digit-by-digit substitution with no calculation at all, which is precisely the ease of conversion the question is asking about.
3. ASCII: ASCII is a character encoding standard that maps letters, digits, and symbols to numeric codes; it is not a positional number system at all. Comparing hexadecimal-to-ASCII conversion doesn't even make sense in the same way as converting between number bases, so this option describes an unrelated category of thing.
4. BCD: Binary Coded Decimal encodes each decimal digit separately as a 4-bit binary group, which still requires first converting the number to decimal and then encoding each decimal digit. This adds an extra decimal step and complexity, so it is not as direct as the binary relationship.

Only option (B) describes a conversion that is truly direct and calculation-free, because 16 being an exact power of 2 lets each hex digit map onto a fixed 4-bit pattern with no arithmetic involved.

Therefore, the correct answer is binary.