V22.0436 - Prof. Grishman
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
What is the clock period for a 200 Hz clock? For a 200 MHz clock?
You should be able to design a circuit (and compute its propagation
delay), given a verbal or truth-table description of the circuit. You
be familiar with the basic circuit types: and, or, nand, nor,
and not gates; multiplexer, full adder, and decoder.
Design an exclusive-or circuit using only AND, OR, and NOT gates.
What is the delay of this circuit?
Given a 3-bit input X representing a 3-bit binary number, design a
to test whether X is greater than or equal to 5. If this condition is
the output of your circuit should be a 1, otherwise 0. In your design,
refer to the low order bit of X as X0.
Suppose you are given a large box of 2-input multiplexers. Show how to
connect them up to create an 8-input multiplexer. If the delay from
to output on the 2-input multiplexer is 10 ns, what is the delay of the
circuit you have designed? Suppose you had to create an N input
what would the delay be? How many 2-input multiplexers would you need?
You should understand the function of the basic types of flip-flops
(set-reset, D type, master-slave), and the reason for using
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
a state transition table, and finally a circuit.
Go through the process of designing a two-bit down counter.
draw the state diagram. Second, write down the state transition table.
Third, convert the transition table to a formula in Boolean algebra.
convert the formula to a circuit and show how it would connect to FFs
create a complete counter circuit.
Consider a two-bit up counter with a select input S. If S=0,
circuit acts as an up counter; if S=1, the counter goes to 0 on the
clock cycle (reset). Give the state transition diagram and table for
counter. Design the counter circuit from this table.
You should understand two's complement arithmetic and the design of
adders and subtractors.
What is the 16-bit, two's complement representation of -3? Give your
Suppose you are given an adder for unsigned 16-bit binary numbers. What
changes must you make to the circuit to use it as an adder for 16-bit,
two's complement numbers?
The mid-term is Wednesday,