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Convert (23)8 into its decimal number.
- a)18
- b)8
- c)19
- d)7
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Convert (23)8 into its decimal number.a)18b)8c)19d)7Correct answer is ...
Octal to Decimal Conversion:
- Step 1: Since an octal number only uses digits from 0 to 7, we first arrange the octal number with the power of 8.
- Step 2: We evaluate all the power of 8 values such as 80 is 1, 81 is 8, etc., and write down the value of each octal number.
- Step 3: Final step is to add the product of all the numbers to obtain the decimal number.
Application:
Step 1: Write 23 with the power of 8. Start from the right-hand side.
2 × 81 + 3 × 80
Step 2: Evaluate the power of 8 values for each octal number.
16 + 3 = 19 (Decimal Number)
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Convert (23)8 into its decimal number.a)18b)8c)19d)7Correct answer is ...
To convert the octal number (23)8 into its decimal equivalent, we can use the positional value system. The positional value system states that each digit in a number represents a certain power of the base, which in this case is 8.
The octal number (23)8 can be expanded as follows:
(23)8 = 2 × 8^1 + 3 × 8^0
Calculating the powers of 8, we have:
8^1 = 8
8^0 = 1
Substituting the values into the expanded form, we get:
(23)8 = 2 × 8 + 3 × 1
Simplifying further, we have:
(23)8 = 16 + 3
Adding the values together, we get:
(23)8 = 19
Therefore, the decimal equivalent of the octal number (23)8 is 19.
The octal number (23)8 can be expanded as follows:
(23)8 = 2 × 8^1 + 3 × 8^0
Calculating the powers of 8, we have:
8^1 = 8
8^0 = 1
Substituting the values into the expanded form, we get:
(23)8 = 2 × 8 + 3 × 1
Simplifying further, we have:
(23)8 = 16 + 3
Adding the values together, we get:
(23)8 = 19
Therefore, the decimal equivalent of the octal number (23)8 is 19.
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Convert (23)8 into its decimal number.a)18b)8c)19d)7Correct answer is option 'C'. Can you explain this answer?
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