Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > The decimal value 0.25a)s equivalent to the b...
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The decimal value 0.25
- a)s equivalent to the binary value 0.1
- b)is equivalent to the binary value 0.01
- c)is equivalent to the binary value 0.00111...
- d)cannot be represented precisely in binary
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The decimal value 0.25a)s equivalent to the binary value 0.1b)is equiv...
1st Multiplication Iteration Multiply 0.25 by 2
0.25 x 2 = 0.50(Product) Fractional part=0.50
Carry=0 (MSB)
2nd Multiplication Iteration
Multiply 0.50 by 2
0.50 x 2 = 1.00(Product) Fractional part = 1.00
Carry = 1(LSB)
The fractional part in the 2nd iteration becomes zero and hence we stop the multiplication iteration.
Carry from the 1st multiplication iteration becomes MSB and carry from 2nd iteration becomes LSB
So the Result is 0.01
0.25 x 2 = 0.50(Product) Fractional part=0.50
Carry=0 (MSB)
2nd Multiplication Iteration
Multiply 0.50 by 2
0.50 x 2 = 1.00(Product) Fractional part = 1.00
Carry = 1(LSB)
The fractional part in the 2nd iteration becomes zero and hence we stop the multiplication iteration.
Carry from the 1st multiplication iteration becomes MSB and carry from 2nd iteration becomes LSB
So the Result is 0.01
Most Upvoted Answer
The decimal value 0.25a)s equivalent to the binary value 0.1b)is equiv...
Explanation:
Decimal to Binary Conversion:
To convert a decimal number to binary, we follow the steps given below:
1. Divide the decimal number by 2.
2. Record the remainder of the division.
3. Divide the quotient obtained in step 1 by 2.
4. Record the remainder of the division.
5. Continue the process until the quotient becomes 0.
6. The binary number is obtained by writing the remainders obtained in reverse order.
For example, let's convert 0.25 to binary:
1. 0.25 * 2 = 0.5 (quotient = 0, remainder = 0.5)
2. 0.5 * 2 = 1.0 (quotient = 1, remainder = 0)
3. The quotient is 1, so we stop.
4. The binary number is 0.01.
Binary to Decimal Conversion:
To convert a binary number to decimal, we follow the steps given below:
1. Write down the binary number.
2. Assign a weight to each digit, starting from the rightmost digit and doubling the weight for each subsequent digit.
3. Multiply each digit by its weight and add up the results.
4. The sum obtained in step 3 is the decimal equivalent of the binary number.
For example, let's convert 0.1 to decimal:
1. The binary number is 0.1.
2. The weight of the rightmost digit (1) is 2^(-1) = 0.5.
3. Multiply each digit by its weight and add up the results:
0.1 * 0.5 = 0.05
4. The decimal equivalent of the binary number is 0.05.
Answer:
The decimal value 0.25 is equivalent to the binary value 0.01 because we can convert 0.25 to binary by dividing 0.25 by 2 and recording the remainder until the quotient becomes 0. The resulting binary number is 0.01. Similarly, we can convert 0.1 to decimal by multiplying each digit by its weight and adding up the results. The decimal equivalent of 0.1 is 0.05. Therefore, option B is the correct answer.
Decimal to Binary Conversion:
To convert a decimal number to binary, we follow the steps given below:
1. Divide the decimal number by 2.
2. Record the remainder of the division.
3. Divide the quotient obtained in step 1 by 2.
4. Record the remainder of the division.
5. Continue the process until the quotient becomes 0.
6. The binary number is obtained by writing the remainders obtained in reverse order.
For example, let's convert 0.25 to binary:
1. 0.25 * 2 = 0.5 (quotient = 0, remainder = 0.5)
2. 0.5 * 2 = 1.0 (quotient = 1, remainder = 0)
3. The quotient is 1, so we stop.
4. The binary number is 0.01.
Binary to Decimal Conversion:
To convert a binary number to decimal, we follow the steps given below:
1. Write down the binary number.
2. Assign a weight to each digit, starting from the rightmost digit and doubling the weight for each subsequent digit.
3. Multiply each digit by its weight and add up the results.
4. The sum obtained in step 3 is the decimal equivalent of the binary number.
For example, let's convert 0.1 to decimal:
1. The binary number is 0.1.
2. The weight of the rightmost digit (1) is 2^(-1) = 0.5.
3. Multiply each digit by its weight and add up the results:
0.1 * 0.5 = 0.05
4. The decimal equivalent of the binary number is 0.05.
Answer:
The decimal value 0.25 is equivalent to the binary value 0.01 because we can convert 0.25 to binary by dividing 0.25 by 2 and recording the remainder until the quotient becomes 0. The resulting binary number is 0.01. Similarly, we can convert 0.1 to decimal by multiplying each digit by its weight and adding up the results. The decimal equivalent of 0.1 is 0.05. Therefore, option B is the correct answer.
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The decimal value 0.25a)s equivalent to the binary value 0.1b)is equivalent to the binary value 0.01c)is equivalent to the binary value 0.00111...d)cannot be represented precisely in binaryCorrect answer is option 'B'. Can you explain this answer?
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