Hex-by-hex subtraction by bytes Compute the three independent byte differences: 47 − 25, 34 − 1C, FA − 2F. Present the result as three hex bytes separated by spaces.

Difficulty: Easy

Correct Answer: 22 18 CB

Explanation:


Introduction / Context:
Byte-wise subtraction is frequent in low-level programming and protocol parsing. Treating each pair as an independent eight-bit subtraction with base-16 arithmetic sharpens comfort with hex digits and borrows.



Given Data / Assumptions:

  • Operate on bytes: (47 − 25), (34 − 1C), (FA − 2F).
  • All values are hexadecimal (base 16).
  • Each subtraction is performed independently.


Concept / Approach:
Subtract nibble-by-nibble with proper borrowing in base 16, where A=10 through F=15. No cross-byte borrowing occurs because each pair is separate.



Step-by-Step Solution:
47 − 25: 0x47 − 0x25 = (71 − 37)₁₀ = 34₁₀ = 0x22.34 − 1C: 0x34 − 0x1C = (52 − 28)₁₀ = 24₁₀ = 0x18.FA − 2F: 0xFA − 0x2F = (250 − 47)₁₀ = 203₁₀ = 0xCB.


Verification / Alternative check:
Perform column-wise hex subtraction with borrows: A−F requires borrow; confirms 0xCB for the last byte, while the first two differences are straightforward without long borrow chains.



Why Other Options Are Wrong:
Any variation such as 22 17 CB, 22 19 CB, 22 18 CC, or 21 18 CB results from nibble borrow mistakes or decimal-hex confusion.


Common Pitfalls:
Treating a borrow as 10 instead of 16 in hex, or confusing C=12 and F=15 when subtracting.



Final Answer:
22 18 CB

More Questions from Digital Arithmetic Operations and Circuits

Discussion & Comments

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