What is the biased exponent in this example, expressed as decimal?

Question

Question 10

To find the IEEE-754 SP floating point representation of the binary number 0.0000111, one first shifts the

decimal point to the (left or right) by right, 5 places.

 

 

Question 11

(Continuing problem #10) What is the biased exponent in this example, expressed as decimal?

  -5

 

  -4

 

  123

 

  None of these

 

  122

 

Answer 1

To convert from binary to decimal, multiply each digit in 0.0000111 by its place value. In this case, the decimal equivalent is 2^-5 + 2^-6 + 2^-7. We store the "-5", or the exponent corresponding to the MSB (which you found in Question 10), as a biased exponent, because it is signed. In order to account for the sign, add 127 to -5 according to the IEEE standard. Then, the biased exponent expressed as a decimal is 122.