1. Convert the following decimal fractions to binary with a maximum of six places to the right of the binary…

1. Convert the following decimal fractions to binary with a maximum of six places to the right of the binary point:

a) 298.796875

b) 16.1240234375

2. Represent the following decimal numbers in binary using 8-bit signed magnitude one’s complement, and two’s complement:

a) 77

b) -42

3. If the floating point number representation on a certain system has a signed bit, a 3-bit exponent, and a 4-bit      significant:

What is the largest positive and the smallest positive number that can be stored on this system if the storage is normalized?(Assume no bits are implied, there is no biasing, exponents use two’s complement notation, and exponents of all zeros and all ones are allowed)

4. Assume we are using the simple model for floating-point representation as given in this book ( the representation uses a 14-bit format, 5 bits for the exponent with a bias of 16, a normalized mantissa of 8 bits, and a single sign bit for the number):

a) Show how the computer would represent the numbers 100.00 and 0.25 using this floating-point format.

b) Show how the computer would add the two floating-point numbers in part a by changing one of the numbers so they are both expressed using the same power of 2.

c) Show how the computer would represent the sum in part b using the given floating-point representation. What decimal value for the sum is the computer actually storing? Explain.

5. Show how each of the following floating- point values would be stored using IEEE-754 single precision (be sure to indicate the sign bit, the exponent, and the significant fields):

a) 0.75

b) 26.625