Page 35 - Computer Science Class 11 Without Functions
P. 35
In contrast, the decimal number system is a positional number system. For example, in the numbers 234, 6249, and
5482, the symbol 4 denotes the values four, forty, and four hundred, respectively. Thus, the decimal number system
is a positional number system. We already know that the decimal representation of a number comprises a string of
symbols, each symbol being a decimal digit that takes one of the values: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. The value of a symbol
within a number depends on its relative position addition. Each symbol (also called a decimal digit) within a number
has an associated place value, as described below:
Face Value: The value of a symbol in the number system is called its face value. Thus, in the decimal system, the
symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 have the face values zero, one, two, three, four, five, six, seven, eight, and nine,
respectively.
Place Value: In decimal number systems, the value of a digit within a number depends on the position of the digit.
For example,
○ The rightmost digit is called the one's digit or unit digit (value 10 = one),
0
1
○ The second digit from the right end is called the tens digit (value 10 = ten),
2
○ The third digit from the right end is called the hundreds digit (value 10 = hundred),
3
○ The fourth digit from the right end is called the thousands digit (value 10 = thousand),
4
○ The fifth digit from the right end is called the ten thousand digit (value 10 = ten thousand),
5
○ The sixth digit from the right end is called the hundred thousand digit (value 10 = hundred thousand),
6
○ The seventh digit from the right end is called the millions digit (value 10 = million), and so on.
Now, consider the number 1352. In this number,
○ Digit 2 represents 2 units (2 × 1)
1
○ Digit 5 represents 5 tens (5 × 10 )
○ Digit 3 represents 3 hundreds (3 × 10 )
2
3
○ Digit 1 represents 1 thousands (1 × 10 )
Hence the numeric value represented by the number 1352 can be calculated as:
2
3
1 × 10 + 3 × 10 + 5 × 10 + 2 × 10
0
1
= 1 × 1000 + 3 × 100 + 5 × 10 + 2 × 1 = (1352) 10
Table 2.1 shows the digit's place value, face value, and value represented by the decimal number (1352) .
10
Table 2.1: Digit's place value, face value, value represented by (1352) .
10
Digit's place value thousand (1000) hundred (100) ten (10) Unit (1)
Digit 1 3 5 2
Face value 1 3 5 2
Value represented 1 × 10 3 3 × 10 2 5 × 10 1 2 × 10 0
by digit
1. Give the face value of each occurrence of the digit 4 in the number 284849.
2. Give the place value of each digit in the number 284849.
In the number 1352, digit 1 has the highest place value, it is known as Most Significant Digit (MSD). Similarly, as digit
2 carries the minimum place value, so it is known as Least Significant Digit (LSD). In general, in a positional number
system, the leftmost digit is the most significant, and the rightmost digit is the least significant digit.
Now, let us look at fractional numbers. A fractional number consists of an integer part (also called an integral part)
and a fraction part (also called a fractional part). Note that 0<= fraction part<1. A dot called a radix point separates the
integer part from the fractional part.
Number Systems and Encoding Schemes 33

