Question

5p Question 5 Convert the decimal number 9.625 to a floating-point number expressed in the 14-bit simple model given in your text (1 bit for the sign, 5 bits for exponent using excess-15 notation, and 8 bit mantissa with no implied bit).

Answer 1

Given decimal number = 9.625

Convert the given number to Binary number=1001.101 = 1.001101 X 2^3

The floating point number is of the format = (1.M) X 2^(E - B)

Where M is Mantissa , E is Exponent and B is Bias

Sign - 0 (Positive)

Exponent - Bias= 3

Exponent - 15= 3 ------------> Exponent = 3+15=18 --------> Binary form of Exponent = 10010

Mantissa = 001101 ----------> If we represent Mantissa in 8 bits then Mantissa = 00110100

Floating point number has 14 bits, which can be represented as below

Sign(1 bit)

Exponent(5 bits)

Mantissa(8 bits)

So, the floating point representation is

0

10010

00110100

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