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Using the IEEE 754 floating point format, write down the bit pattern that would represent -1/4.
Can you represent -1/4 exactly?
Solution
-1/4=-0.25
The value of a IEEE-754 number is computed as:
sign * 2exponent * mantissa
sign is negative so sign bit is=1
The sign is stored in bit 32. The exponent can be computed from bits 24-31 by subtracting 127.
The mantissa (also known as significand or fraction) is stored in bits 1-23. An invisible leading
bit (i.e. it is not actually stored) with value 1.0 is placed in front, then bit 23 has a value of 1/2,
bit 22 has value 1/4 etc. As a result, the mantissa has a value between 1.0 and 2. If the exponent
reaches -127 (binary 00000000), the leading 1 is no longer used to enable gradual underflow
by using above we can find
IEEE 754 floating point format of-1/4=-0.25:
10111110100000000000000000000000
hex decimal format:
0xbe800000

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Using the IEEE 754 floating point format, write down the bit pattern .pdf

  • 1. Using the IEEE 754 floating point format, write down the bit pattern that would represent -1/4. Can you represent -1/4 exactly? Solution -1/4=-0.25 The value of a IEEE-754 number is computed as: sign * 2exponent * mantissa sign is negative so sign bit is=1 The sign is stored in bit 32. The exponent can be computed from bits 24-31 by subtracting 127. The mantissa (also known as significand or fraction) is stored in bits 1-23. An invisible leading bit (i.e. it is not actually stored) with value 1.0 is placed in front, then bit 23 has a value of 1/2, bit 22 has value 1/4 etc. As a result, the mantissa has a value between 1.0 and 2. If the exponent reaches -127 (binary 00000000), the leading 1 is no longer used to enable gradual underflow by using above we can find IEEE 754 floating point format of-1/4=-0.25: 10111110100000000000000000000000 hex decimal format: 0xbe800000