largest negative real number represented using IEEE floating point

Question

So I want to find the largest negative real number that can be represented using the IEEE-754 floating point.

So far I know the sign bit should be 1, and mantissa is 11111111, and the exponent is 255. I just put them into the formula, then I get -1.11111111 x 2^128.

The answer is -3.403 x 10^38.

How do I transform what I have into the answer form ?

What are you expecting? A code? or the correct answer? or an algorithm? — Arun A S
– Arun A S, Commented Apr 18, 2015 at 6:38
"... and mantissa is 11111111, and the exponent is 255. ..." is not correct. and -1.11111111(base2) x 2^128 --> -6.792355...e+38 — chux
– chux, Commented Apr 18, 2015 at 6:40
just do your math. Multiplicate what you found - if you can't do in memory, use your calculator and type -1.11111111 x 2^128. Which will give you a different number than you are expected. — mfro
– mfro, Commented Apr 18, 2015 at 6:44

user3386109 · Accepted Answer · 2015-04-18 07:03:23Z

4

From this wikipedia article the formula for calculating the value from the bit pattern is

enter image description here

The largest negative number will have

sign bit = 1
mantissa = all 1's
exponent = 254

_{Note that an exponent of 255 is reserved for special cases like infinity and NAN.}

Plugging those values into the formula, we get

enter image description here

which can be written as

value = (-1)(1 + 0.5 + 0.25 + 0.125 + ... + 2^-23)(2^127)
      = (-1)(2)(2^127)  // since the sum is approximately 2
      = -(2^128)    
      = -3.403 x 10^38  // says my calculator

answered Apr 18, 2015 at 7:03

user3386109

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4 Comments

Mark Dickinson Over a year ago

@user2998413: It looks pretty good to me. What do you think is wrong with it?

chux Over a year ago

@user2998413 Aside from maybe considering "largest negative real number" as -INF, this answer does well describe finding the largest finite negative bianry32. "IEEE-754 floating point" does have other floating point types with finite values about -10*pow(10,6144). Other than that, your comment needs explanation.

user3386109 Over a year ago

@user2998413 It's hard to improve the answer unless you tell me why you think it's wrong.

SparkleGoat Over a year ago

Are any of them reserved? Usually it's first and last

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