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 topic of this question is Number System characteristics and their practical applications in computing. It asks for the primary reason why hexadecimal (Base-16) is preferred over other systems like decimal (Base-10) when working with computer data. This involves understanding how memory addresses and machine-level instructions are structured in hardware.
Step 2: Key Formulas and approach:
The key concept is the power-of-two relationship: $16 = 2^4$. This means that one hexadecimal digit perfectly encapsulates four binary bits.
The approach to answering this question is to look at how data is translated between human-readable formats and machine-level formats. Binary strings are often very long and difficult for humans to parse (e.g., a 32-bit address), and hexadecimal serves as a direct, condensed shorthand for these binary strings.
Step 3: Detailed Explanation:}

Digital systems operate on binary (0s and 1s), but a 64-bit instruction is nearly impossible for a programmer to read without making errors.

Hexadecimal provides a way to compress these binary strings. Because each hex digit represents exactly four bits (a nibble), the conversion doesn't require complex multiplication or division like decimal conversion does.

For example, the binary $1111$ is simply $F$ in hex. The binary $0000$ is $0$. To convert $11110000$ to hex, you just write $F0$.

This 1-to-4 mapping allows developers to visualize bit patterns easily. If you see a hex value, you can instantly know which bits are "on" or "off."

Converting from hex to decimal, however, requires calculating powers of 16 ($16^0, 16^1, 16^2$, etc.), which is significantly more difficult to do mentally.

Therefore, the primary advantage is this seamless, "by-inspection" conversion to and from the binary system.

Step 4: Final Answer:
The main advantage of the hexadecimal system is the ease of conversion to and from the binary system.

Answer 2

Let's verify the ease of hexadecimal-to-binary conversion by working through an actual example rather than just stating the rule.

Take the hexadecimal number \( (2F)_{16} \).
Each hex digit is converted to its 4-bit binary equivalent on its own, independent of the other digits:
\( 2 \) becomes \( 0010 \)
\( F \) (which equals 15) becomes \( 1111 \)
Placing these groups side by side in order gives \( (2F)_{16} = (00101111)_2 \).

Notice that no multiplication, division, or repeated remainder calculation was needed at any stage. Compare this to converting \( (2F)_{16} \) to decimal, where you must compute \( 2 \times 16 + 15 = 47 \), an actual arithmetic operation. The binary conversion instead only required knowing four fixed bit patterns for the digits 2 and F.

This works because \( 16 = 2^4 \), so every possible hex digit (0 through F) has exactly one corresponding 4-bit pattern, and stringing these patterns together reconstructs the binary number exactly, with the reverse process (grouping binary digits into fours) working just as directly.

Therefore, the correct answer is binary.