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how to solve this

in Digital Logic by Junior (647 points) | 231 views
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when E=255 and M=0 it denotes special value +infinity or - infinity.

when E=255 and M !=0 it denotes NAN.

so option b and c are eliminated.

don't know about a and d option.
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Here while storing in 32 bit format E = 130+127 = 257.. which will overflow..  but what to do further?
+1
Exponent overflow: A positive exponent exceeds the maximum possible exponent value. In some systems, this may be designated as + infinity or - infinity.

Source:William Stallings.
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so answer should be option b?
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No. (d) only.
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why ?  please elaborate.
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I dont know about special value + infinity.

1 Answer

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Infinities

The infinities of the extended real number line can be represented in IEEE floating-point datatypes, just like ordinary floating-point values like 1, 1.5, etc. They are not error values in any way, though they are often (but not always, as it depends on the rounding) used as replacement values when there is an overflow. Upon a divide-by-zero exception, a positive or negative infinity is returned as an exact result. An infinity can also be introduced as a numeral (like C's "INFINITY" macro, or "∞" if the programming language allows that syntax).

IEEE 754 requires infinities to be handled in a reasonable way, such as

  • (+∞) + (+7) = (+∞)
  • (+∞) × (−2) = (−∞)
  • (+∞) × 0 = NaN – there is no meaningful thing to do

So, it will round to +infinite . https://en.wikipedia.org/wiki/Floating-point_arithmetic

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