1. Represent decimal numbers 109 and -120 in 8-bit two's complement and add them.

2. 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 15, a normalized mantissa of 8 bits, and a single sign bit for the number). a) Show how the computer would represent the numbers 5.49 and 20.5 using this floating-point format. b) Show how the computer would add and multiply these two floating-point numbers.

3. 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 significand fields): a) Smallest positive normalized floating point number b) Smallest positive denormalized floating point number c) Zero d) Inf e) NaN

4. Suppose we are using the Hamming Algorithm presented in the text as an error-correcting code that will allow all single-bit errors to be corrected. We now receive the following code word (n=9): 0 0 1 0 1 0 0 0 1 Assuming even parity, is this a legal code word? If not, according to our error-correcting code, where is the error and what is the correct data word?

5. Show that xz + x'y' + y'z' = xz + y' using a) Truth Table b) Boolean Identities (show your steps and give the names of identities used).

6. Given the function: F(x,y,z)= y(x'z + xz') + x(yz + yz') a) List the truth table for F. b) Draw the logic diagram using the original Boolean expression c) Simplify the expression using Boolean Identities. d) List the truth table for your answer in Part c. e) Draw the logic diagram for the simplified expression in Part c.

7. Write (x + y)(x' + y' + z) in Sum of Products Canonical Form