Asked Dec 18, 2019

Express 384 in IEEE 32-bit floating-point format.


Expert Answer

Step 1

Representing 384 in IEEE 32-bit floating-point format:

Step 1: Convert the given number “384” to its equivalent binary number. 384 is equivalent to “11000000”.

Step 2: Normalize the binary value as “1.1000000”.

Step 3: Consider the 23 bits after decimal point. i.e., consider the bits after decimal point from step 2 and thereafter pad with zero’s up to 23 bits. Thus, corresponding mantissa = “100000000000000000000000”.

Step 4: Write down the exponent value by doing bias adjustment.

  • Count number of digits after decimal point in step 2.
  • Add those digits to 127.
  • Therefore, 2 digits are there after decimal point.

Bias = 8+127


  • 135 in binary is “10000111” (Exponent)
Step 2

Floating-point format:...


Image Transcriptionclose

Fractional part Exponent 31 30 23 22 0 10000111 100000000000000000000000


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