Chapter 2- Number System Conversion and Boolean Logic
Number system
Computer
is an electronic data processing machine.
It
processes all types of data in the binary digits such as 1
or 0. It also performs
mathematical calculation in
different format.
Number
system is the most important in the computer
system or day – to- day live
activities for counting and
calculating any numeric problems.
A
number system is the series of number used to
represent the value of any
things. It is also used to count
any countable things.
Four different types of number system.
Binary
number system
Decimal
number system
Octal
number system
Hexadecimal
number system
The
number system is classified into different categories on the basis of number of
digits
used.
Each
number system has a base also called a radix.
A
decimal number system is a system of base 10, binary is a system of base 2,
octal is a
system of base 8 and hexadecimal
is a system of base 16.
Number
conversion
The
process of converting a number from one base to another is called number
conversion.
We
can convert binary number system to decimal number system and vice versa.
Similarly
all other number system can be converted to one another.
.
|
Base |
Symbols/
Digits used |
|
|||||||||||||||
|
Binary |
2 |
0 |
1 |
||||||||||||||
|
Octal |
8 |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
||||||||
|
Decimal |
10 |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
||||||
|
Hexa decimal |
16 |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
A |
B |
C |
D |
E |
F |
Book's Exercise Page number 97
Exercisess
1. Multiple Choice
Questions:
a)………..number system have base 16.
i.
Octal
ii.
Binary
iii.
Decimal
iv.
Hexadecimal
b) BIT stands for…………..
i.
Binary Information
Technology
ii.
Binary
Digit
iii.
Bus Information
Technology
iv.
Binary Integer
c) Computer uses.......
number system to process data.
i.
Octal
ii.
Binary
iii.
Decimal
iv.
Hexadecimal
d) 1's complement of
10101 is………….
i.
01010
ii.
1010
iii.
10101
iv.
01011
e) The octal number 502
is equal to …………..in decimal number system.
i.
321
ii.
322
iii.
205
iv.
323
f) The binary number
111001001100 is equal to……………. in hexadecimal number system.
i.
C4E
ii.
D4B
iii.
E4C
iv.
B4D
g) 2's complement of
10011 is…………………..
i.
01100
ii.
11001
iii.
01101
iv.
1101
h) The number system
having radix 10 is …………….Number system.
i.
Octal
ii.
Binary
iii.
Decimal
iv.
Hexadecimal
i)
2's complement of 10111 is............
i.
01000
ii.
1000
iii.
1001
iv.
01001
j)The
sum of 10111 and 11001 is…………………
i.
11000
ii.
110000
iii.
101100
iv.
110001
k)
10101x110 is……………………
i.
1111110
ii.
101011
iii.
10111
iv.
100011
2 Short Answer Questions:
a.
What is number system? List its type.
A
number system is a way to represent numbers using a set of symbols and rules.
Types
of number systems:
Decimal (Base 10)
Binary (Base 2)
Octal (Base 8)
Hexadecimal (Base 16)
b.
What is binary number system? Write its base.
The
binary number system uses only two digits: 0 and 1. It is commonly used in
computers and digital systems. Its base is 2
c.
What is decimal number system? List the digits used in decimal number system.
The
decimal number system is the standard system for denoting integer and
non-integer numbers.
Digits
used: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Its base is 10
d.
What is hexadecimal number system? Write its radix.
The
hexadecimal number system uses 16 symbols: 0–9 and A–F (where A=10, B=11, ...,
F=15).
Its
Radix (Base) is 16
e.
What is octal number system? List the digits used in octal number system.
The
octal number system uses eight digits from 0 to 7. It is commonly used in
computer systems.
Digits
used: 0, 1, 2, 3, 4, 5, 6, 7. Its base is 8
f.
Define 1's complement and 2's complement.
1's Complement: It is the binary number
obtained by inverting all bits (changing 0 to 1 and 1 to 0) of a given binary
number.
2's Complement: It is obtained by adding 1 to
the 1's complement of a binary number. It is commonly used to represent
negative numbers in binary.
3. Convert the following binary number into decimal number.
a. 111101
b. 111010
c. 110.1011
d. 11011.11
e. 110111.1101
4. Convert the following decimal number into binary number.
a. 329
b. 578.64
c. 137
d. 95.23
e. 101.297
5. Convert the following octal number into decimal number.
a. 751
b. 632.371
c. 3426
d. 256.410
e. 5732
6. Convert the following decimal number into octal number.
a. 611
b. 577.784
c. 1430.321
d. 629
e. 2341
7. Convert the following hexadecimal number into decimal number.
a. 396A
b. AC9.B41
C. 537E
d. 6320.AF2
8. Convert the following decimal number into hexadecimal number.
a. 467
b. 273.931
c. 654.271
d. 831
e. 5679.401
9.Convert
the following binary number into octal number.
a.1011101
b.11101.101111
c.1010110.1100011
d.10111001
e.1011101
10
Convert the following octal number into binary number
a.532
b.
5670
c.15021.524
d.
732.3164
e.73544
11.
Convert the following binary number into hexadecimal number
a
10111101
b.
1110110
c.
10011101.1011101
d.
101000111.101111100
e.
101111110
12.
Convert the following hexadecimal number into binary number.
a.CEOF
b.
1A89.DC2
C.
FA52
d.
A57DC
e.
C98.A52
13.
Convert the following hexadecimal number into octal number.
a.
CAFE
b.
378B.C5A
C.
FACE
d.
ADC.30E66
e.
56D
14.
Convert the following octal number into hexadecimal number.
a.
5741
b.
5124
c.
311.572
d.
5221.3216
e.
1101101
15.
Solve the following binary addition problems:
a.
11011 + 10110
b.11110
+ 11001
c.
10101 + 11101
d.11101
+ 10111 + 11110
e.101110+110011+10111
f.1011011+
1010111+ 1100111
16.
Solve the following binary subtraction problems:
a.10111-1011
b.110100-11011
c.11101-10011
d.101100-11011
e.101011-11011
f.11111010-1001111
17.
Solve the following binary subtraction problems by using 1's complement and 2's
complement method.
a.1011-11110
b.
11011-1011
c.
11001-10011
d.
10111110111
e.
10111-11011
f.
111011-10111