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The following bit pattern represents a floating point number in IEEE 754 single precision format
1 10000011 101000000000000000000000
The value of the number in decimal form is
- a)-10
- b)-13
- c)-26
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The following bit pattern represents a floating point number in IEEE 7...
Sign bit is 1 -> number is negative
Exponent bits- 10000011
Exponent is added with 127 bias in IEEE single precision format.
So, Actual exponent = 10000011 - 127 = 131 - 127 = 4
Mantissa bits- 101000000000000000000000
In IEEE format, an implied 1 is before mantissa, and hence the actual number is
-1.101 * 24
=- (11010)2 = - 26
Exponent bits- 10000011
Exponent is added with 127 bias in IEEE single precision format.
So, Actual exponent = 10000011 - 127 = 131 - 127 = 4
Mantissa bits- 101000000000000000000000
In IEEE format, an implied 1 is before mantissa, and hence the actual number is
-1.101 * 24
=- (11010)2 = - 26
Most Upvoted Answer
The following bit pattern represents a floating point number in IEEE 7...
Explanation:
The given bit pattern is in IEEE 754 single precision format, which has a total of 32 bits. The leftmost bit represents the sign of the number, the next 8 bits represent the exponent, and the remaining 23 bits represent the mantissa.
In this case, the leftmost bit is 1, which indicates a negative number. The exponent is represented by the next 8 bits, which are 10000011. This is equivalent to 131 in decimal form. However, the exponent is biased by 127, so the actual exponent value is 131 - 127 = 4.
The mantissa is represented by the remaining 23 bits, which are 10100000000000000000000. To convert this to decimal form, we add a leading 1 to the beginning of the mantissa and then interpret the remaining bits as the fractional part of a binary number. In this case, the leading 1 gives us 1.10100000000000000000000 in binary form.
To convert this to decimal form, we multiply each digit by the corresponding power of 2 and add up the results. For example, the first digit after the decimal point is 1/2, the second digit is 1/4, and so on. Doing this calculation, we get:
1.10100000000000000000000 = 1 × 2^0 + 1/2 × 2^-1 + 0/4 × 2^-2 + 1/8 × 2^-3 + 0/16 × 2^-4 + ... = 1.625
Putting it all together, we get:
-1 × 1.625 × 2^4 = -26
Therefore, the value of the number in decimal form is -26.
The given bit pattern is in IEEE 754 single precision format, which has a total of 32 bits. The leftmost bit represents the sign of the number, the next 8 bits represent the exponent, and the remaining 23 bits represent the mantissa.
In this case, the leftmost bit is 1, which indicates a negative number. The exponent is represented by the next 8 bits, which are 10000011. This is equivalent to 131 in decimal form. However, the exponent is biased by 127, so the actual exponent value is 131 - 127 = 4.
The mantissa is represented by the remaining 23 bits, which are 10100000000000000000000. To convert this to decimal form, we add a leading 1 to the beginning of the mantissa and then interpret the remaining bits as the fractional part of a binary number. In this case, the leading 1 gives us 1.10100000000000000000000 in binary form.
To convert this to decimal form, we multiply each digit by the corresponding power of 2 and add up the results. For example, the first digit after the decimal point is 1/2, the second digit is 1/4, and so on. Doing this calculation, we get:
1.10100000000000000000000 = 1 × 2^0 + 1/2 × 2^-1 + 0/4 × 2^-2 + 1/8 × 2^-3 + 0/16 × 2^-4 + ... = 1.625
Putting it all together, we get:
-1 × 1.625 × 2^4 = -26
Therefore, the value of the number in decimal form is -26.
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The following bit pattern represents a floating point number in IEEE 754 single precision format1 10000011 101000000000000000000000The value of the number in decimal form isa)-10b)-13c)-26d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?
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