Representation of floating point (14bit)

0
votes

sign 1 bit, exponent 5 bit, fraction 8bit (I think it's IEEE 754 Standard)

What is the largest decimal value and smallest value that can be represented using above 14 bit float?

isn't 0 11111 11111111 and 1 11111 11111111? if not what would be the answer?

can someone explain in detail?

And what should be smallest value but bigger than zero.

1
floating-pointrepresentation
This question is impossible to answer on the information given: just telling us the number of exponent bits and number of fraction bits does not determine the floating-point format. Is this an IEEE 754-like format? Is it even a binary format? (It could be hexadecimal, for example. I'm assuming not, but you don't say.) Is the significand always normalised? Is the significand considered to be in the form 1.fraction or 0.fraction, or something else? What's the exponent bias? Is there a reserved exponent for infinities and nans? Is there a reserved exponent for subnormals and zeros? - Mark Dickinson
What do you mean by "smallest largest decimal"? How is your representation defined? Similar to IEEE754 (with normals/denormals, infinities/NaNs, exponent-bias, ...)? - chtz
I'm sorry I didn't write down the problem properly. I looked at the problem again. The format follows the IEEE754, and the exponent bias is 15... about significand .. I think it follow format of 1.fraction. - JUN_0

1 Answers

1
votes

Following the IEEE-754 pattern for binary formats, with 1 sign bit, a 5-bit exponent biased by 15, and 8 bits for the primary significand field:

  • The smallest value that can be represented is −∞, with bits 1 11111 00000000.
  • The smallest finite value that can be represented is −230−15•1.111111112 = −215•(2−2−8) = −(216−27 = −(65536-128) = −65,408, with bits 1 11110 11111111.
  • The smallest positive value that can be represented is +21−15•0.000000012 = +2−14•2−8 = +2−22, with bits 0 00000 00000001.
  • The largest finite value that can be represented is the negation of the smallest finite value, shown above: +230−15•1.111111112 = +215•(2−2−8) = +(216−27 = +(65536-128) = +65,408, with bits 0 11110 11111111.
  • The largest value that can be represented is +∞, with bits 0 11111 00000000.

What is the largest decimal value…

Binary floating-point numbers represent a set of real numbers. They do so using binary digits, effectively being binary numerals. They do not represent decimal values per se and do not have decimal digits. Their values can be shown using decimal numerals, as shown above.