Which one of the given options is the correct conversion value of the number (4ED)₁₆ in...
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Which one of the given options is the correct conversion value of the number (4ED)₁₆ in binary format?
Show answer & explanation
Answer: A. 0100 1110 1101
To convert hexadecimal (4ED)₁₆ to binary, convert each hex digit independently to its 4-bit binary equivalent: 4 = 0100, E = 1110, D = 1101. Concatenating these gives 0100 1110 1101. This is the standard direct conversion method for hex-to-binary conversion.
Step-by-step Derivation:
Step-by-step hex to binary conversion:
Convert each hexadecimal digit to 4-bit binary:
- 4 (hex) = 0100 (binary)
- E (hex) = 14 (decimal) = 1110 (binary)
- D (hex) = 13 (decimal) = 1101 (binary)
Concatenate the binary groups in order:
0100 | 1110 | 1101Final binary result: 0100 1110 1101
Verification (convert back to hex):
0100 = 4, 1110 = E, 1101 = D → (4ED)₁₆ ✓