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The decimal floating-point number -40.1 represented using IEEE-754 32-bit representation and written in hexadecimal form is _____
- a)0xC2206000
- b)0xC2006666
- c)0xC2006000
- d)0xC2206666
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
The decimal floating-point number -40.1 represented using IEEE-754 32-...
32-bit floating-point representation of a binary number in IEEE- 754 is
In IEEE-754 format, 32-bit (single precision)
(-1)s × 1.M × 2E – 127
Calculation:
Convert: 40.1 to binary
Step 1: convert 40
(40)10 = (101000)2
Step 2: convert .1 to binary
0.1 × 2 = 0.2 (0)
0.2 × 2 = 0.4 (0)
0.4 × 0.2 = 0.8 (0)
0.8 × 0.2 = 1.6 (1)
0.6 × 0.2 = 1.2 (1)
0.2 × 0.2 = 0.4 (0) and so on
Given binary number is
(40.1)10 = (101000.000110011001100…)2
(40.1)10 = 1.0100 0000 1100 1100 … × 25
Signed (1 bit) = 1 (given number is negative)
Exponent (8 bit) = 5 + 127 = 132
∴ Exponent = (132)10 = (1000 0100)2
Mantissa (23 bits ) = 0100 0000 1100 1100 1100 110
(1100 0010 0010 0000 0110 0110 0110 0110)2 = (C2206666)16
(C2206666)16 = 0xC2206666
In IEEE-754 format, 32-bit (single precision)
(-1)s × 1.M × 2E – 127
Calculation:
Convert: 40.1 to binary
Step 1: convert 40
(40)10 = (101000)2
Step 2: convert .1 to binary
0.1 × 2 = 0.2 (0)
0.2 × 2 = 0.4 (0)
0.4 × 0.2 = 0.8 (0)
0.8 × 0.2 = 1.6 (1)
0.6 × 0.2 = 1.2 (1)
0.2 × 0.2 = 0.4 (0) and so on
Given binary number is
(40.1)10 = (101000.000110011001100…)2
(40.1)10 = 1.0100 0000 1100 1100 … × 25
Signed (1 bit) = 1 (given number is negative)
Exponent (8 bit) = 5 + 127 = 132
∴ Exponent = (132)10 = (1000 0100)2
Mantissa (23 bits ) = 0100 0000 1100 1100 1100 110
(1100 0010 0010 0000 0110 0110 0110 0110)2 = (C2206666)16
(C2206666)16 = 0xC2206666
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Community Answer
The decimal floating-point number -40.1 represented using IEEE-754 32-...
Conversion of -40.1 to IEEE-754 32-bit Representation:
- The decimal number -40.1 can be represented as: -1 * (1.010012) * 2^5
- The sign bit is '1' for negative numbers
- The exponent is calculated as bias + 5 = 127 + 5 = 132 which is 10000100 in binary
- The mantissa is 01000000 00011001 10011001 (normalized form)
- Combining the sign bit, exponent, and mantissa, we get the IEEE-754 32-bit representation:
11000001001000000000110011001100
Conversion to Hexadecimal:
- Split the binary representation into groups of 4 bits:
1100 0001 0010 0000 0000 1100 1100 1100
- Convert each group of 4 bits to hexadecimal:
C 1 2 0 0 C C C
- Combine the hexadecimal values:
C1200CCC
Therefore, the hexadecimal representation of -40.1 in IEEE-754 32-bit format is 0xC1200CCC which corresponds to option 'D'.
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The decimal floating-point number -40.1 represented using IEEE-754 32-bit representation and written in hexadecimal form is _____a)0xC2206000b)0xC2006666c)0xC2006000d)0xC2206666Correct answer is option 'D'. Can you explain this answer?
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