An 9-bit floating-point number representation system has the following specifica

Question

An 9-bit floating-point number representation system has the following specification:

Among the 8 bits(B8,B7,B6,B5,B4,B3,B2,B1,B0 ), bit B8 is the sign bit, bits B7,B6,B5,B4 is the exponent with a bias value (0100). Bits B3,B2,B1,B0  consist of the mantissa. The binary number that is represented is (-1)B8 * (0. ,B3,B2,B1,B0) * 10B7B6B5B4 - 0100.

A)What are the largest positive and negative numbers this system can present?

B)Find a postive number x whic is representable by this system such that 1 + x = 1.

C)Find the largest positive number y which is representable by this system such that 1 + y = 1

Explanation / Answer

Ans )

   a-   Largest positive number =
           0 for positive signed bit.
           Bias value = 0100 = 4
           Max 4 bit exponent = 1111 = 15
           Exponent = 1111 - 0100 = 1011 = 11
           Max mantissa value = 1111 = 15
           As max mantissa is greater than 10 so there will be a carry of 1 to exponent.
           Therefore,    exponent = 1011 + 0001 = 1100 = 12
                       mantissa = 0111 = 7
           Final = 011000111   = +(12.7)10
          
       Similarly, largest negative value
           Largest negative = 111000111 = -(12.7)10
      
   b-   1 + x = 1
       x = 1 - 1 = 0
       x = 000000000 = 010
      
   c-   1 + y = 1
       y = 1 - 1 = 0
       y = 000000000 = 010

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