GATE CS 2014 Set 2 — Question 55
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Digital Logic → Number Systems & Arithmetic → IEEE 754 Floating Point
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Question
The value of a float type variable is represented using the single-precision 32-bit floating point format of IEEE-754 standard that uses 1 bit for sign, 8 bits for biased exponent and 23 bits for mantissa. A float type variable is assigned the decimal value of . The representation of in hexadecimal notation is
Correct answer
(A) C1640000H
Solution
Value:
Sign | Exponent | Mantissa
1 | 10000010 | 11001000000000000000000Grouping into Hex:
1100 | 0001 | 0110 | 0100 | 0000 | 0000 | 0000 | 0000
C | 1 | 6 | 4 | 0 | 0 | 0 | 0Result: C1640000H
1.Sign bit: Negative, so .
2.Binary representation:
3.Normalization:
4.Exponent: Actual exponent is . Bias is .
Stored Exponent 5.Mantissa: (23 bits, dropping the implicit leading 1)
32-bit Representation:Sign | Exponent | Mantissa
1 | 10000010 | 11001000000000000000000Grouping into Hex:
1100 | 0001 | 0110 | 0100 | 0000 | 0000 | 0000 | 0000
C | 1 | 6 | 4 | 0 | 0 | 0 | 0Result: C1640000H
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