1. (50 points) Computer Arithmetic

(a) (15 points) Assume we have a 16-bit Arithmetic Logic Unit. List the inputs and outputs in

binary for the ALU if we are using it to determine if X = 1810 < Y = 2510. Remember: the

ALU has three inputs and three outputs. The selection value will be 112 for Set on Less Than.

Use 16 bits or 1 bit to represent the remaining inputs and outputs as appropriate

(b) (15 points) Compare and contrast the third multiplication algorithm with Booths Algorithm

for the following 8-bit numbers. Use A = 0001 00112 for the multiplier and B = 0011 11102 for

the multiplicand. Determine AxB using each algorithm. Which algorithm uses more arithmetic

operations? Which algorithm is more efficient for AxB? Recall that shifts are more efficient

than adds.

(c) (20 points) Suppose you are constructing a 3-bit ripple counter using three D flip-flops and

some selection of gates. The inputs to the system are Reset (sets every output to zero) and Inc

(a signal to increment the counter). The outputs are the value of the counter C2C1C0. When

the counter has the value 7 and is incremented, it should become zero. Draw the D flip-flop

and logic gates for C2 (the most significant bit) only. You may use a block diagram for the D

flip-flop.

Notes:

1(a) Inputs are X (16 bit), Y (16 bit), Selection Value (11_2) which is already specified. Outputs are Zero (1 bit), Result (16 bit), Overflow (1 bit) As long as you provide inputs (X, Y), and outputs (Zero, Result, Overflow), you get full credit. 1(c) You need to create a truth table with inputs of C2, C1, C0, and output of C2; Then write a logic function of C2 = F(C2, C1, C0). Based on the logic function, you will be able to draw the block diagram.