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The decimal equivalent of the binary number 10110.0101011101 is
- a)22.2408216500
- b)22.3408216750
- c)22.3408213125
- d)22.3408203125
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
The decimal equivalent of the binary number 10110.0101011101 isa)22.24...
Conversion of Binary to Decimal
To convert a binary number to its decimal equivalent, we have to follow the steps given below:
Step 1: Write the binary number.
Step 2: Starting from the right-hand side, we assign each digit a position value of 2 to the power of n, where n starts from 0 on the right-hand side and increases by 1 for each subsequent digit to the left.
Step 3: Multiply each digit by its position value.
Step 4: Add all the products obtained in step 3.
Calculation
10110.0101011101 can be written as:
1 × 2^4 + 0 × 2^3 + 1 × 2^2 + 1 × 2^1 + 0 × 2^0 + 0 × 2^-1 + 1 × 2^-2 + 0 × 2^-3 + 1 × 2^-4 + 0 × 2^-5 + 1 × 2^-6 + 0 × 2^-7 + 1 × 2^-8 + 1 × 2^-9 + 0 × 2^-10 + 1 × 2^-11
= 16 + 0 + 4 + 2 + 0 + 0.25 + 0.25 + 0 + 0.0625 + 0 + 0.015625 + 0 + 0.00390625 + 0.0009765625 + 0 + 0.000244140625
= 22.3408203125 (Option D)
Therefore, the correct answer is option D, 22.3408203125.
To convert a binary number to its decimal equivalent, we have to follow the steps given below:
Step 1: Write the binary number.
Step 2: Starting from the right-hand side, we assign each digit a position value of 2 to the power of n, where n starts from 0 on the right-hand side and increases by 1 for each subsequent digit to the left.
Step 3: Multiply each digit by its position value.
Step 4: Add all the products obtained in step 3.
Calculation
10110.0101011101 can be written as:
1 × 2^4 + 0 × 2^3 + 1 × 2^2 + 1 × 2^1 + 0 × 2^0 + 0 × 2^-1 + 1 × 2^-2 + 0 × 2^-3 + 1 × 2^-4 + 0 × 2^-5 + 1 × 2^-6 + 0 × 2^-7 + 1 × 2^-8 + 1 × 2^-9 + 0 × 2^-10 + 1 × 2^-11
= 16 + 0 + 4 + 2 + 0 + 0.25 + 0.25 + 0 + 0.0625 + 0 + 0.015625 + 0 + 0.00390625 + 0.0009765625 + 0 + 0.000244140625
= 22.3408203125 (Option D)
Therefore, the correct answer is option D, 22.3408203125.
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The decimal equivalent of the binary number 10110.0101011101 isa)22.2408216500b)22.3408216750c)22.3408213125d)22.3408203125Correct answer is option 'D'. Can you explain this answer?
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