Hexadecimal in digital design — “Hex is commonly used as a shorthand to represent strings of bits.” Judge the statement.

Difficulty: Easy

Correct Answer: Correct

Explanation:


Introduction / Context:
Hexadecimal (base 16) maps neatly to binary because 16 = 2^4; each hex digit corresponds to exactly four bits. Designers and programmers rely on hex to write and read binary values in a compact, human-friendly form, especially for registers, bitmasks, addresses, and machine code bytes.

Given Data / Assumptions:

  • Binary is verbose in text; hex compresses 4 bits into one symbol (0–9, A–F).
  • Use cases include memory dumps, microcontroller registers, and protocols.
  • Radix prefixes like 0x or h'...' identify hex literals in many contexts.


Concept / Approach:
Since each nibble (4 bits) is one hex digit, converting between binary and hex is grouping bits by fours. This one-to-one mapping reduces transcription errors and accelerates debugging. Octal (base 8) similarly maps groups of three bits, but hex dominates due to byte alignment (8 bits = 2 hex digits).

Step-by-Step Solution:

Group a binary string into nibbles from the LSB side.Map each group of four to a hex digit (0000→0, …, 1111→F).Write the hex sequence as a compact representation of the same bits.


Verification / Alternative check:

Round-trip: Convert hex back to binary by replacing each hex digit with its 4-bit pattern.


Why Other Options Are Wrong:

Incorrect: Contradicts standard engineering practice.Only for signed integers: Hex applies to any bit pattern, signed or unsigned.Used only in assembly: Hex pervades firmware, hardware, and high-level tooling alike.


Common Pitfalls:

Dropping leading zeros in the most significant nibble and changing byte alignment.Confusing endianness with hex representation; endianness affects byte order, not digit meaning.


Final Answer:

Correct

More Questions from Number Systems and Codes

Discussion & Comments

No comments yet. Be the first to comment!
Join Discussion