Tutorial Questions
(a) What is the largest binary
number that can be expressed with 24 bits? What are the equivalent decimal and
hexadecimal number?
(b) Determine the base/radix of the numbers in
each case for the following operations to be correct:
(i) 29 + 17 = 40 (ii) 7 + 6
= 15 (iii) 67 + 24 = 113
(c) Covert the hexadecimal number AD54 to
binary, and then convert it from binary to octal
(d) Convert the decimal number 198 to binary in
two ways: (a) convert directly to binary; (b) convert first to hexadecimal and
then from hexadecimal to binary. Which method is faster?
(e) Express the following numbers in decimal:
(i) (10110.0101)2 (ii)
(69.8)16 (ii) (73.65)
(iv) (1110.0101)2 (v)
(BEBE.C)16
(f)
Differentiate between Analog and Digital electronic system with respect
to the following concept; i.
Signal ii.
Representation of value.
iii. Technology/Technique iv.
Response to noisev. Uses/Application.
(g)
Number systems are characterized by the following;
i.
The number of independent digits used in the number system.
ii.
The place value of different digits constituting a value in the system.
iii.
The maximum number that can be written with a given number of digits. Explain these characteristics with respect to the following number systems using arbitrary
examples;
1.
Decimal
2. Octal 3.
Hexadecimal 4. Binary.
(h) Determine the base/radix (number system) of the number in each case for the
following operation to be correct.
i.
29+17
= 40
ii.
7+6
= 15
iii.
67+24+133
(i)
Solve each of the following using comfortable number of bits subtraction
problems using 2’s complement arithmetic.
i. 011111112 - 7810
ii. 001100102
- 12310
iii.
010010012 - 11110
iv.
(3E91)16 – (1DEF)16
(j) Write out the expression for the Boolean function bellow;
(k) Simplify the expression in (i), and hence implement the logic circuit for the simplified expression.
(l) Show that;(k) Simplify the expression in (i), and hence implement the logic circuit for the simplified expression.
(m) In a scenario to design a bank vault lock; there are three (3) key holders to the lock; the manager, senior bank officer, and a cashier. To open the vault, at least two (2) keys (i.e. two key holders) must be available. If the cashier is to open the vault, the managers’ key must be available. Design a logic circuit to implement the vault lock following these procedure;
1.
Define the input and output variables.
2.
Obtain the Boolean expression for the lock
3.
Simplify the expression obtained in (ii)
4.
Design the logic circuit for the vault lock.
