Computer Science 281

Exercise set #3

Due: Wednesday, Feb. 18 (in class)

1, Suppose that X = 0xFFFFA456 and that Y = 0xFFFFB645. Calculate

X AND Y

X OR Y

X XOR Y

X NAND Y

X NOR Y

2. Convert 110 from base 10 into binary, and from there to octal and hexadecimal

3. Write down (in hex) the 2’s complement representation of 25 and of –25

4. Suppose that X = 0x13 and Y = 0x6. Convert both to binary, and perform the following operations:

X+ Y

X– Y

X* Y

X/ Y (give quotient and remainder)

5. Write the truth table for (not X)(not Y) + (Not X)Y and using the truth table construct the circuit for the expression using AND, OR, and NOT gates. Can you see a way to simplify the circuit?

6. Wire the 3 – 8 multiplexer to implement the majority function. Do not write down the circuit for the multiplexer – indicate it by a box with 8 inputs, three address lines and one output. The circuit should compute the majority of the address lines A, B, and C.

7. Use DeMorgan’s laws to simplify the following expressions (i.e., negations are moved next to the variables, double negations are eliminated):

NOT ((NOT A) OR B)

NOT ((A OR B) AND NOT (A AND B)) (Careful with parenthesis’s! This is the same as NOT (A XOR B)).