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A floating-point (FP) number is said to be normalized, if the most significant bit of the mantissa is
- a)1
- b)0
- c)-1
- d)2
Correct answer is option 'A'. Can you explain this answer?
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A floating-point (FP) number is said to be normalized, if the most sig...
A floating-point (FP) number is said to be normalized, if the most significant bit of the mantissa is 1.
- If the exponent is all zeros, the floating point number is denormalized and the most significant bit of the mantissa is known to be zero.
- The floating number representation has four parts:1. The first part represents a single fixed point number is called the mantissa.
- The second part designates the position of the decimal point and is called the exponent.
- The mantissa always a positive number holds the significant digits of the floating point number.
- The exponent indicates the positive or negative power of the radix that the mantissa and sign should be multiplied by.
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A floating-point (FP) number is said to be normalized, if the most sig...
Explanation:
In floating-point representation, a normalized number is a number that is represented in scientific notation, where the most significant bit (MSB) of the mantissa is always 1. This means that the mantissa is in the form of 1.xxxxx, where xxxxx represents the fractional part of the number.
Why is the most significant bit of the mantissa always 1 in a normalized floating-point number?
The reason behind having the most significant bit of the mantissa always set to 1 is to maximize the precision of the floating-point representation. By setting the MSB to 1, we ensure that the maximum possible number of bits is available to represent the fractional part of the number.
Significance of the most significant bit:
The most significant bit of the mantissa determines the magnitude of the number. By setting it to 1, the number is shifted to the left, increasing its magnitude. This allows for a larger range of values to be represented using a fixed number of bits.
Normalized form:
In normalized form, the most significant bit is always 1, and the mantissa is represented as 1.xxxxx. This means that the range of possible values for the mantissa is [1, 2). By choosing this range, we can represent a larger number of values using the same number of bits.
Benefits of normalization:
1. Increased precision: By setting the most significant bit to 1, we maximize the number of bits available to represent the fractional part of the number, increasing the precision of the representation.
2. Efficient representation: Normalized floating-point numbers allow for a wider range of values to be represented using a fixed number of bits. This makes them more efficient for storage and computation purposes.
3. Simplified arithmetic operations: Normalized numbers simplify arithmetic operations like addition, subtraction, multiplication, and division, as they align the decimal points.
Conclusion:
In conclusion, a floating-point number is said to be normalized when the most significant bit of the mantissa is set to 1. This representation maximizes precision, allows for efficient storage and computation, and simplifies arithmetic operations.
In floating-point representation, a normalized number is a number that is represented in scientific notation, where the most significant bit (MSB) of the mantissa is always 1. This means that the mantissa is in the form of 1.xxxxx, where xxxxx represents the fractional part of the number.
Why is the most significant bit of the mantissa always 1 in a normalized floating-point number?
The reason behind having the most significant bit of the mantissa always set to 1 is to maximize the precision of the floating-point representation. By setting the MSB to 1, we ensure that the maximum possible number of bits is available to represent the fractional part of the number.
Significance of the most significant bit:
The most significant bit of the mantissa determines the magnitude of the number. By setting it to 1, the number is shifted to the left, increasing its magnitude. This allows for a larger range of values to be represented using a fixed number of bits.
Normalized form:
In normalized form, the most significant bit is always 1, and the mantissa is represented as 1.xxxxx. This means that the range of possible values for the mantissa is [1, 2). By choosing this range, we can represent a larger number of values using the same number of bits.
Benefits of normalization:
1. Increased precision: By setting the most significant bit to 1, we maximize the number of bits available to represent the fractional part of the number, increasing the precision of the representation.
2. Efficient representation: Normalized floating-point numbers allow for a wider range of values to be represented using a fixed number of bits. This makes them more efficient for storage and computation purposes.
3. Simplified arithmetic operations: Normalized numbers simplify arithmetic operations like addition, subtraction, multiplication, and division, as they align the decimal points.
Conclusion:
In conclusion, a floating-point number is said to be normalized when the most significant bit of the mantissa is set to 1. This representation maximizes precision, allows for efficient storage and computation, and simplifies arithmetic operations.
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A floating-point (FP) number is said to be normalized, if the most significant bit of the mantissa isa)1b)0c)-1d)2Correct answer is option 'A'. Can you explain this answer?
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