Discussion
What is the decimal equivalent of the hexadecimal number 2F?
Answer: B
Correct answer: 47
Each hexadecimal digit carries a place value that is a power of 16, read from the right: \( 16^{0} = 1 \) and \( 16^{1} = 16 \). In 2F the digit F stands for 15, so \[ 2 \times 16 + 15 = 32 + 15 = 47. \] The letters run A = 10, B = 11, C = 12, D = 13, E = 14, F = 15, and it is worth memorising them, since almost every hexadecimal question depends on the conversion. A quicker route for small values goes through binary. Each hexadecimal digit is four bits: 2 is 0010 and F is 1111, giving 00101111, which is \( 32 + 8 + 4 + 2 + 1 = 47 \). Conversion by grouping is faster than arithmetic once the sixteen four-bit patterns are familiar. The largest two-digit hexadecimal number is FF, which is 255 - the maximum value of one byte, and the reason colour codes and byte values are so often written this way.
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