Given below are two statements. In the light of the above statements, choose the correct answer from the options given below.
Statement I:The decimal number 43.25 equals the binary number 101011.01.
Statement II:The binary number 1110.111 equals the decimal number 14.625.
ABoth Statement I and Statement II are true
BBoth Statement I and Statement II are false
CStatement I is true but Statement II is false ✓ Correct
DStatement I is false but Statement II is true
Correct answer: (C) Statement I is true but Statement II is false
Explanation
Statement 1 is correct because binary 101011.01 equals decimal 43.25, since 101011 is 43 and .01 is one-quarter.
Statement 2 is incorrect because binary 1110.111 equals decimal 14.875, not 14.625.
In the first value the integer part sums 32 plus 8 plus 2 plus 1, giving 43.
In the second value the fraction .111 adds one-half, one-quarter and one-eighth, giving 0.875.
Each place after the binary point halves in value, as 0.5, 0.25 and 0.125.
A small slip in the fractional bits changes the decimal result noticeably.
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