Which of the following statement(s) is/are TRUE? S1: The decimal number 11 is larger than the hexadecimal number 11. S2: In the binary number 1110.101, the fractional part has the decimal value as 0.625.
S2 only
To determine which of the statements S1 and S2 is true, let's evaluate them one by one:
- Statement S1: "The decimal number 11 is larger than the hexadecimal number 11."
- In decimal, the number 11 is simply 11.
- In hexadecimal, the number 11 represents \(1 \times 16^1 + 1 \times 16^0 = 16 + 1 = 17\) in decimal.
- Therefore, decimal 11 is not larger than hexadecimal 11, as 11 < 17.
- S1 is False.
- Statement S2: "In the binary number 1110.101, the fractional part has the decimal value as 0.625."
- The binary number 1110.101 can be broken down as follows:
- Integer part (1110): \(1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 0 \times 2^0 = 8 + 4 + 2 + 0 = 14\)
- Fractional part (0.101):
- \(1 \times 2^{-1} = 0.5\)
- \(0 \times 2^{-2} = 0\)
- \(1 \times 2^{-3} = 0.125\)
- Adding up the fractional part: \(0.5 + 0 + 0.125 = 0.625\)
- S2 is True.
- The binary number 1110.101 can be broken down as follows:
Therefore, the correct answer is "S2 only," making the correct option: S2 only.
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