NCERT Solutions for Class 9th Maths Chapter 1 Number Systems Exercise 1.3 Question 1

Number Systems

Decimal

Here’s the decimal number system as an example:

digits (or symbols) allowed: 0-9

base (or radix): 10

the order of the digits is significant

345 is really

3 x 100 + 4 x 10 + 5 x 1

3 x 10^2 + 4 x 10^1 + 5 x 10^0

3 is the most significant symbol (it carries the most weight)

5 is the least significant symbol (it carries the least weight)

Binary

Here’s a binary number system:

digits (symbols) allowed: 0, 1

base (radix): 2

each binary digit is called a BIT

the order of the digits is significant

numbering of the digits

msb lsb

n-1 0

where n is the number of digits in the number

msb stands for most significant bit

lsb stands for least significant bit

1001 (base 2) is really

1 x 2^3 + 0 x 2^2 + 0 x 2^1 + 1 x 2^0

9 (base 10)

11000 (base 2) is really

1 x 2^4 + 1 x 2^3 + 0 x 2^2 + 0 x 2^1 + 0 x 2^0

24 (base 10)

Of interest: most assembly languages have no way to represent

binary values!

Octal

Here’s an octal number system:

digits (symbols) allowed: 0-7

base (radix): 8

the order of the digits is significant

345 (base 8) is really

3 x 8^2 + 4 x 8^1 + 5 x 8^0

192 + 32 + 5

229 (base 10)

1001 (base 8) is really

1 x 8^3 + 0 x 8^2 + 0 x 8^1 + 1 x 8^0

512 + 0 + 0 + 1

513 (base 10)

Hexadecimal

here’s a hexadecimal number system:

digits (symbols) allowed: 0-9, a-f

base (radix): 16

the order of the digits is significant

hex decimal binary

0 0 0000

1 1 0001

.

.

.

9 9 1001

a 10 1010

b 11 1011

c 12 1100

d 13 1101

e 14 1110

f 15 1111

a3 (base 16) is really

a x 16^1 + 3 x 16^0

160 + 3

163 (base 10)