Points: : 40 points
PART I (8 POINTS)
Assume that X consists of 3 bits, x2, x1, and x0. Write four logic functions that are true if and
(A) X contains only one 0
(B) X contains an even number of 0s
(C) X when interpreted as an unsigned binary number is less than 4
(D) X when interpreted as a signed (two’s complement) number is negative
PART II (8 POINTS)
With x = 01011011 (bin) and y = 00001101(bin) representing two’s complement signed integers,
perform, showing all work:
(A) x + y
(B) x – y
(C) x * y
PART III (6 POINTS)
Do the unsigned multiply for 0011 * 0111, using the Multiply Algorithm Version 3 (check the
lecture notes). Show the contents of registers for multiplicand (4 bits) and product (8 bits) step
PART IV (6 POINTS)
Do the unsigned multiply for 0011 * 0111, using the Booth’s Algorithm (check the lecture notes).
Show the contents of registers for multiplicand (4 bits) and product (8 bits) step by step.
PART V (6 POINTS)
In Lecture Notes c335-ALU-1.pdf, we discussed how we could modify the 4-bit ALU to
support detecting overflow but did not give the proof. Now you are expected to prove you
can detect overflow by simply check if Carry into MSB ! = Carry out of MSB.
Hint: you could use a table (like a truth table) to list all situations, then identify the cases that
PART VI (6 POINTS)
Do necessary modifications on the following 1 bit ALU, then use it to construct a 4-bit
ALU that supports the SLT instruction.
Hint: read text appendix B section B.5 to find clue.