V22.0436  Prof. Grishman
Practice MidTerm
Note: the italicized comments indicate the main topics to be covered
on the exam, but are not exhaustive. Any topic covered in the notes
about combinational and sequential circuits is
fair game on the exam.
Time and Frequency
You should know the units of time and frequency, and be able to
convert
between them.

What is the clock period for a 200 Hz clock? For a 200 MHz clock?
Combinational Circuits
You should be able to design a circuit (and compute its propagation
delay), given a verbal or truthtable description of the circuit. You
should
be familiar with the basic circuit types: and, or, nand, nor,
exclusiveor,
and not gates; multiplexer, full adder, and decoder.

Design an exclusiveor circuit using only AND, OR, and NOT gates.
What is the delay of this circuit?

Given a 3bit input X representing a 3bit binary number, design a
circuit
to test whether X is greater than or equal to 5. If this condition is
true,
the output of your circuit should be a 1, otherwise 0. In your design,
refer to the low order bit of X as X_{0}.

Suppose you are given a large box of 2input multiplexers. Show how to
connect them up to create an 8input multiplexer. If the delay from
input
to output on the 2input multiplexer is 10 ns, what is the delay of the
circuit you have designed? Suppose you had to create an N input
multiplexer;
what would the delay be? How many 2input multiplexers would you need?
Sequential Circuits
You should understand the function of the basic types of flipflops
(setreset, D type, masterslave), and the reason for using
masterslave
FFs. You should be able to assemble a register file. From a description
of a sequential procedure, you should be able to create a state
diagram,
a state transition table, and finally a circuit.

Go through the process of designing a twobit down counter.
First,
draw the state diagram. Second, write down the state transition table.
Third, convert the transition table to a formula in Boolean algebra.
Finally,
convert the formula to a circuit and show how it would connect to FFs
to
create a complete counter circuit.

Consider a twobit up counter with a select input S. If S=0,
the
circuit acts as an up counter; if S=1, the counter goes to 0 on the
next
clock cycle (reset). Give the state transition diagram and table for
this
counter. Design the counter circuit from this table.
Arithmetic
You should understand two's complement arithmetic and the design of
adders and subtractors.

What is the 16bit, two's complement representation of 3? Give your
answer
in binary.

Suppose you are given an adder for unsigned 16bit binary numbers. What
changes must you make to the circuit to use it as an adder for 16bit,
two's complement numbers?
The midterm is Wednesday,
October 11.