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Encoding Schemes and Number System · Class 11 · CBSE · Science Computer Science

Convert the hexadecimal number (2F)16 into its decimal equivalent and its 8-bit binary equivalent. Also state why hexadecimal notation is convenient…

Practice question from Encoding Schemes and Number System (Class 11 · CBSE · Science Computer Science), with the correct answer and a step-by-step solution.

hard · Subjective · Q-6942F3

Convert the hexadecimal number (2F)16 into its decimal equivalent and its 8-bit binary equivalent. Also state why hexadecimal notation is convenient for representing binary data.

Answer: (2F)16 equals 2 × 16 + 15 = 47 in decimal. Each hexadecimal digit represents four binary bits, so (2F)16 is 0010 1111 in 8-bit binary. Hexadecimal is convenient because it represents binary data compactly, with one hexadecimal digit corresponding exactly to four bits.

Solution

For the decimal conversion, (2F)16=2×16+15=47(2F)_{16} = 2 \times 16 + 15 = 47. The hexadecimal digits 2 and F correspond to 0010 and 1111, giving 00101111. Hexadecimal notation is compact because every hexadecimal digit maps directly to four binary bits.

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