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The decimal number (57.375)10 when converted to binary number takes the form:
- a)(111001.011)2
- b)(100111.110)2
- c)(110011.101)2
- d)(111011.011)2
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The decimal number (57.375)10 when converted to binary number takes th...
Concept:
Decimal to binary:
- Take decimal number as dividend.
- Divide the number by 2.
- Get the integer quotient for the next iteration.
- Get the remainder (it will be either 0 or 1 because of divisor 2).
- Repeat the steps until the quotient is equal to 0
- Write the remainders in reverse order (which will be equivalent binary number of given decimal number).
Decimal to binary: (fractional part)
- Take decimal number as multiplicand.
- Multiple this number by 2 (2 is base of binary so multiplier here).
- Store the value of integer part of result in an array (it will be either 0 or 1 because of multiplier 2).
- Repeat the above two steps until the number became zero.
- Write these resultant integer part
Calculation:
Binary of 57:
Now, write remainder from bottom to up (in reverse order), this will be 111001 which is equivalent binary number of decimal integer 57.
Convert decimal fractional number 0.375 into binary number.
Here, decimal fraction: 0.375
Now, write these resultant integer part, this will be 0.0110 which is equivalent binary fractional number of decimal fractional 0.375.
∴ 57.375 can be written as 111001.011 in binary
Hence, option (1) is correct.
Binary of 57:
Now, write remainder from bottom to up (in reverse order), this will be 111001 which is equivalent binary number of decimal integer 57.
Convert decimal fractional number 0.375 into binary number.
Here, decimal fraction: 0.375
Now, write these resultant integer part, this will be 0.0110 which is equivalent binary fractional number of decimal fractional 0.375.
∴ 57.375 can be written as 111001.011 in binary
Hence, option (1) is correct.
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Community Answer
The decimal number (57.375)10 when converted to binary number takes th...
To convert a decimal number to a binary number, we can use the method of successive division by 2. Here's how we can convert the decimal number (57.375)10 to its binary equivalent:
1. Convert the integer part:
- Divide 57 by 2: 57 ÷ 2 = 28, remainder 1
- Divide 28 by 2: 28 ÷ 2 = 14, remainder 0
- Divide 14 by 2: 14 ÷ 2 = 7, remainder 0
- Divide 7 by 2: 7 ÷ 2 = 3, remainder 1
- Divide 3 by 2: 3 ÷ 2 = 1, remainder 1
- Divide 1 by 2: 1 ÷ 2 = 0, remainder 1
Reading the remainders from bottom to top, the binary equivalent of the integer part is 111001.
2. Convert the fractional part:
- Multiply the fractional part (0.375) by 2: 0.375 × 2 = 0.75
- Multiply the fractional part (0.75) by 2: 0.75 × 2 = 1.5
- Multiply the fractional part (0.5) by 2: 0.5 × 2 = 1.0
Reading the whole numbers from left to right, the binary equivalent of the fractional part is 011.
3. Combine the integer and fractional parts:
Putting the integer part and the fractional part together, we get the binary representation of (57.375)10 as 111001.011.
Therefore, the correct answer is option A, (111001.011)2.
1. Convert the integer part:
- Divide 57 by 2: 57 ÷ 2 = 28, remainder 1
- Divide 28 by 2: 28 ÷ 2 = 14, remainder 0
- Divide 14 by 2: 14 ÷ 2 = 7, remainder 0
- Divide 7 by 2: 7 ÷ 2 = 3, remainder 1
- Divide 3 by 2: 3 ÷ 2 = 1, remainder 1
- Divide 1 by 2: 1 ÷ 2 = 0, remainder 1
Reading the remainders from bottom to top, the binary equivalent of the integer part is 111001.
2. Convert the fractional part:
- Multiply the fractional part (0.375) by 2: 0.375 × 2 = 0.75
- Multiply the fractional part (0.75) by 2: 0.75 × 2 = 1.5
- Multiply the fractional part (0.5) by 2: 0.5 × 2 = 1.0
Reading the whole numbers from left to right, the binary equivalent of the fractional part is 011.
3. Combine the integer and fractional parts:
Putting the integer part and the fractional part together, we get the binary representation of (57.375)10 as 111001.011.
Therefore, the correct answer is option A, (111001.011)2.
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The decimal number (57.375)10 when converted to binary number takes the form:a)(111001.011)2b)(100111.110)2c)(110011.101)2d)(111011.011)2Correct answer is option 'A'. Can you explain this answer?
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