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V22.0436 - Prof. Grishman

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Practice Mid-Term

*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.*

The mid-term is open book and open notes. However, you may not
use your computer during the exam; only printed notes are alliwed.

#### 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 truth-table description of the circuit. You
should
be familiar with the basic circuit types: and, or, nand, nor,
exclusive-or,
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 if the delay of each individual gate
is 200 ps?
- Given a 3-bit input X representing a 3-bit 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 2-input multiplexers. Show
how to
connect them up to create an 8-input multiplexer. If the delay from
input
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
multiplexer;
what would the delay be? How many 2-input multiplexers would you need?

####
Sequential Circuits

*You should understand the function of the basic types of flip-flops
(set-reset, D type, master-slave), and the reason for using
master-slave
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 two-bit
*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 two-bit
*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, including the carry-look-ahead adder, and be
able to give the delay time of these circuits.*
- What is the 16-bit, two's complement representation of -3? Give
your
answer
in binary.
- 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?
- Given AND, OR, NOT gates and full adders, design a circuit for
doing 4-bit two's complement subtraction.
- A sum-of-products circuit has a propagation delay = 3 gate
delays. Why can't we build a 16-bit adder using sum-of-products
with this propagation delay?

#### MIPS

You should be able to translate
simple code segments given in C or Java into MIPS assembler, and answer
questions about the MIPS instruction set.

- Write a sequence of MIPS instructions which put the absolute
value of $2 into $3.
- Write a MIPS instruction which will set $2 to 131,072 (= 2
^{17}
= 0000 0000 0000 0010 0000 0000 0000 0000_{2})

### The mid-term is Tuesday,
October 19th.