Number Systems 447
POINTS TO REMEMBER
R Weightage of any digit is made from its base raised to a power.
R The base is dependent on the number system.
R Place of any digit denotes the power of its base.
REVIEW QUESTIONS
Target the Correct Option
Find in Few Seconds
1. Which of the following computers was based
on decimal number system?
(a) Apple (c) ENIAC
(b) BBC micro (d) none of these
2. The number 7654 cannot belong to _______
number system.
(a) binary (c) hexadecimal
(b) octal (d) none of these
3. The number 1011 may belong to
(a) binary (c) any number system
(b) decimal (d) none of these
4. Which one of the following number systems
has the largest base value?
(a) Octal (c) Hexadecimal
(b) Decimal (d) none of these
5. Which of the following numbers would have
identical representation in any number system?
(a) 1 (c) 4
(b) 2 (d) none of these
6. In which one of the following number system
decimal number 16 would be expressed as 20?
(a) Hexadecimal (c) Binary
(b) Octal (d) None of these
7. To convert from binary to hexadecimal, we
take the groups of _____ binary digits.
(a) 2 (c) 16
(b) 4 (d) none of these
8. Which one of the following symbols is also a
part of hexadecimal representation?
(a) X (c) H
(b) F (d) none of these
9. Which of the following symbols is not a part
of octal representation?
(a) 3 (c) 7
(b) 5 (d) none of these
10. Which one of the following symbols is a part
of decimal and hexadecimal number systems
but not a part of binary and octal number
systems?
(a) 1 (c) 8
(b) 5 (d) none of these
1. How would we express 8275 in decimal?
[Hint. Equation A.2]
2. Why computers are based on binary number
system?
3. Convert 2222 from decimal to binary.
4. What would be the binary equivalent of
ABCD in hexadecimal?
5. Express 1010 0101 (in binary) in hexadecimal
and also in decimal.
6. Convert the octal number 234 into binary,
decimal and hexadecimal.
7. Which representation technique we should
adopt so that we may conclude that 1011 is in
binary, octal, decimal or hexadecimal?
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448 Computer Architecture and Organization
8. Find the missing digit (represented by *) in
the following binary addition.
100*
+ 0001
------
1010
9. Find the missing digit (represented by *) in
the following hexadecimal addition.
AB*D
+ 0010
--------
AC0D
10. Is there any easy method to distinguish
between odd and even binary numbers?
Spend Some Time Here
1. How many digits or symbols should be there
in a quad-number system? What are they?
2. What would be the value (in decimal) of 12 in
quad-number system?
3. Modify the Table A.1 by adding a new col-
umn for quad-number system and ll-up this
new column with all twenty entries.
4. How can we convert from hexadecimal to
decimal and vice versa?
5. Why the base of any number system is always
represented in integers and never in real
numbers?
6. What would be the hexadecimal equivalent of
the following expression?
0 × 8
3
+ 0 × 8
2
+ 3 × 8
1
+ 0 × 8
0
7. To convert from decimal to binary, we keep
on dividing the decimal number by 2. Can we
convert a decimal number to hexadecimal by
dividing it by 16?
8. It is possible to convert from hexadecimal to
binary using the table look-up procedure. Is it
possible to convert from hexadecimal to deci-
mal using table look-up procedure? Justify
your answer.
9. What are the advantages and disadvantages of
binary and hexadecimal representations?
10. It was mentioned that digital logic offer only
two states: on and off. Then why tri-state is
not taken as a third state?
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