The following hexadecimal number (1E.43)16 is equivalent toQuestion 3Answera.(35.503)8b.(35.103)8c.(36.503)8d.(36.103)8
Question
The following hexadecimal number (1E.43)16 is equivalent to
Question 3
Answer
a. (35.503)8
b. (35.103)8
c. (36.503)8
d. (36.103)8
Solution
To answer this question, we first need to convert the hexadecimal number to a decimal number, and then convert the decimal number to an octal number.
Step 1: Convert the hexadecimal number to a decimal number.
The hexadecimal number is 1E.43.
The integer part is 1E. Convert 1E from hexadecimal to decimal:
116^1 + E16^0 = 16 + 14 = 30
The fractional part is .43. Convert .43 from hexadecimal to decimal:
416^-1 + 316^-2 = 0.25 + 0.01171875 = 0.26171875
So, the decimal number is 30.26171875.
Step 2: Convert the decimal number to an octal number.
The integer part is 30. Convert 30 from decimal to octal:
30/8 = 3 remainder 6
So, the octal equivalent of 30 is 36.
The fractional part is .26171875. Convert .26171875 from decimal to octal:
.261718758 = 2.09375 (take the integer part 2) .093758 = 0.75 (take the integer part 0) .75*8 = 6 (take the integer part 6)
So, the octal equivalent of .26171875 is .203.
Therefore, the octal equivalent of the hexadecimal number (1E.43)16 is (36.203)8.
So, the answer is d. (36.103)8.
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