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Radix conversions: Convert the decimal number 43 to (i) hexadecimal and (ii) Binary-Coded Decimal (BCD).

Difficulty: Easy

Correct Answer: 2B, 01000011

Explanation:


Introduction / Context:
Base conversion is a routine but crucial skill in digital systems. Hexadecimal offers compact binary representation, while BCD encodes each decimal digit into a 4-bit nibble, commonly used for displays and decimal arithmetic interfaces.


Given Data / Assumptions:

  • Decimal number: 43.
  • Hexadecimal conversion required.
  • BCD encoding required (4 bits per decimal digit).


Concept / Approach:
For hex: repeatedly divide by 16 or decompose into high and low nibbles. For BCD: encode each decimal digit individually (4 → 0100, 3 → 0011).


Step-by-Step Solution:

Hex: 43 / 16 = 2 remainder 11 (B). So 43₁₀ = 2B₁₆.BCD: '4' → 0100, '3' → 0011, so BCD(43) = 0100 0011.


Verification / Alternative check:
Binary of 43 is 0010 1011; grouping nibbles gives 0x2B. BCD is per digit; concatenation yields 0100 0011 as expected.


Why Other Options Are Wrong:

B2: would correspond to 178 decimal, not 43.00110100 is BCD for 34, not 43.01000100 corresponds to the digits 4 and 4, not 4 and 3.


Common Pitfalls:

Confusing BCD with straight binary; BCD encodes digits, not the entire number's binary form.


Final Answer:

2B, 01000011
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