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The number 6.25 in the decimal notation, when converted to the binary notation will read as ?
Correct answer is '110.01'. Can you explain this answer?
Verified Answer
The number 6.25 in the decimal notation, when converted to the binary ...
Hence, 6 =110
Now 0.25 x 2 = 0.50 → 0
0.50 x 2 = 1.00 → 1
0.00 x 2 = 0 → 0
Hence, 0.25 = 0.010 →1
Hence (6.25)2 = 110.010
The correct answer is: 110.01
Most Upvoted Answer
The number 6.25 in the decimal notation, when converted to the binary ...
Conversion from decimal to binary notation
To convert a decimal number to binary notation, we need to divide the decimal number by 2 repeatedly and keep track of the remainders. The binary representation is obtained by arranging the remainders in reverse order.
Step 1: Division by 2
Start by dividing the decimal number 6.25 by 2. The quotient is 3 and the remainder is 0.
Step 2: Division by 2
Next, divide the quotient from the previous step, which is 3, by 2. The quotient is 1 and the remainder is 1.
Step 3: Division by 2
Divide the quotient from the previous step, which is 1, by 2. The quotient is 0 and the remainder is 1.
Step 4: Binary representation
The binary representation is obtained by arranging the remainders from the previous steps in reverse order. In this case, the remainders are 1, 1, and 0. Therefore, the binary representation of 6.25 is 110.01.
Explanation:
The first remainder obtained in Step 1 represents the least significant bit (LSB) of the binary representation. Each subsequent remainder represents the next bit in increasing order of significance.
In this case, the binary representation is 110.01, where the first 1 represents the value of 2^2 (4), the second 1 represents the value of 2^1 (2), and the 0 represents the value of 2^0 (1). The decimal point separates the whole number part from the fractional part.
The digit 1 in the decimal part represents the value of 2^(-1) (0.5), and the digit 0 represents the value of 2^(-2) (0.25). Adding these values together gives the decimal equivalent of the binary representation, which is 4 + 2 + 0.5 + 0.25 = 6.25.
Therefore, the binary representation of the decimal number 6.25 is 110.01.
To convert a decimal number to binary notation, we need to divide the decimal number by 2 repeatedly and keep track of the remainders. The binary representation is obtained by arranging the remainders in reverse order.
Step 1: Division by 2
Start by dividing the decimal number 6.25 by 2. The quotient is 3 and the remainder is 0.
Step 2: Division by 2
Next, divide the quotient from the previous step, which is 3, by 2. The quotient is 1 and the remainder is 1.
Step 3: Division by 2
Divide the quotient from the previous step, which is 1, by 2. The quotient is 0 and the remainder is 1.
Step 4: Binary representation
The binary representation is obtained by arranging the remainders from the previous steps in reverse order. In this case, the remainders are 1, 1, and 0. Therefore, the binary representation of 6.25 is 110.01.
Explanation:
The first remainder obtained in Step 1 represents the least significant bit (LSB) of the binary representation. Each subsequent remainder represents the next bit in increasing order of significance.
In this case, the binary representation is 110.01, where the first 1 represents the value of 2^2 (4), the second 1 represents the value of 2^1 (2), and the 0 represents the value of 2^0 (1). The decimal point separates the whole number part from the fractional part.
The digit 1 in the decimal part represents the value of 2^(-1) (0.5), and the digit 0 represents the value of 2^(-2) (0.25). Adding these values together gives the decimal equivalent of the binary representation, which is 4 + 2 + 0.5 + 0.25 = 6.25.
Therefore, the binary representation of the decimal number 6.25 is 110.01.
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The number 6.25 in the decimal notation, when converted to the binary notation will read as ?Correct answer is '110.01'. Can you explain this answer?
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