1. Class Exercise 1A

2. Rules
If you believe that you know a correct answer, please raise your hand
I will select one or more students
(independently whether an answer given by
the first student is correct or incorrect)
Please, identify yourself by first name
and give an answer
Correct answer = bonus point 8

3. Problem 1
List all 2-input logic gates that you can recall.

4. Problem 2
How many 2-input logic functions can
be theoretically defined (whether they make
sense or not)?

5. Problem 3
List all 1-input logic gates.

6. Problem 4
What is a minimum set of gates that can
be used to implement all logic functions?

7. Problem 5
List four ways of expressing logic functions.

8. Problem 6
What are the De Morgan’s Laws?
Write their equations and draw their schematic
representation.

9. Problem 7
How many select inputs does an 8-to-1
MUX have?
How many select inputs does an n-to-1

10. Problem 7
How many outputs does a decoder with
two data inputs have?
n data inputs have?

11. Problem 8
Show how to implement a decoder that
recognizes the following 4 ranges of
a 16-bit address A, and generates the
corresponding enable signals e0,e1,e2,e3:
For A in: Assert
C000-CFFF: e0
D000-DFFF: e1
E000-EFFF: e2
F000-FFFF: e3

12. Problem 9
How many inputs does an encoder with
two data outputs have?
n data outputs have?

13. Problem 10
What is a difference between encoder
and priority encoder?

14. Problem 11
Show how to implement Priority Encoder using
multiplexers and a minimum number of
logic gates

15. Problem 12
What is a difference between an
adder, half-adder, and full-adder?

16. Problem 13
Show how to implement Full Adder using
8-to-1 multiplexers only

17. Problem 14
Show how to implement Full Adder using
4-to-1 multiplexers and inverters only

18. Problem 15
What is the width of an output of
a 4x4 unsigned multiplier?
a 4x4 signed multiplier?
a NxN unsigned multiplier?

19. Problem 16
What is the width of an output of
a 4x8 unsigned multiplier?
a 4x8 signed multiplier?
a NxM unsigned multiplier?

20. Problem 17
Give an example of binary inputs to
an unsigned 4x4 multiplier and
a signed 4x4 multiplier
that produce different results.

21. Problem 18
Explain how to perform the following operations
Z = X+Y mod 24
Z = X*Y mod 24
using a 4-bit adder with carry in (cin)
and carry out (cout),
and a 4x4 multiplier, respectively,
where X, Y, and Z are 4-bit variables.

22. Problem 19
Explain how to perform the following
operation using simple arithmetic and
logic circuits:
Y = (X*(2X + 1)) mod 24,
where X and Y are 4-bit variables.

23. Problem 20
Explain using simple diagrams
(based on medium-scale logic components)
how to efficiently perform the following
operations in hardware using combinational
logic only
A. C = A <<< 3
B. C = A <<< B,
where A, B, and C are 8-bit variables.

24. Problem 21
What is a size of a memory with
a 4-bit address input and
an 8-bit data output?
an m-bit address input and
an n-bit data output?

25. Problem 22
Show how to implement Full Adder using ROM
(diagram + contents of ROM)

26. Problem 23
Show how to implement a 3x3 squarer,
implementing equation y = x2,
using ROM (diagram + contents of ROM).

27. Problem 24
Explain how to perform the following
operation using a single-port ROM only:
Y = (X*(2X + 1)) mod 28,
where X and Y are 8-bit variables.
Show the implementation as a ROM,
including the width of the address input and
the width of the data output, as well as the
contents of memory locations with
addresses 0, 1, 8 and 16.

28. Problem 25
What is a function of a tri-state buffer?