TLE 7- QUARTER 1- WEEK 3
COMPUTER NUMBER SYSTEMS:
Humans use words and characters to communicate. We are accustomed to working with numbers, letters, and
words. Computers cannot handle this kind of data, though. Only numbers can be understood by computers.
Computers understand numbers differently from humans, necessitating the need for an entirely other system.
Every time we enter text into a device, the characters are converted into numbers that only the computer can
comprehend.
A computer can comprehend a positional number system, which uses a small number of digits that,
depending on their position in the number, can indicate a variety of values.
A number system is defined as a writing system for denoting numbers logically using digits or symbols.
The following types of number systems are supported by computers.
Binary System
• Octal System
• Decimal System
• Hexadecimal System
The selection of a number system is determined by the particular application and needs of the computer
system. The number system helps to represent numbers in a small symbol set.
Computers use binary number systems because it is the simplest number system to implement using
electronic components.
A binary system can represent all data and instructions in a computer as a combination of 0 and 1, which can
be easily
The number system is a way to represent or express numbers. You have heard of various types of number
systems. In this lesson we will further learn the concepts underlying the difference of this various types.
Binary Number System-is the simplest number system to implement using electronic components.
Only the "on" and "off" states of a switch may be understood by a computer. The numbers 1 and 0 stand for
these two states. Binary numerals are created by fusing the integers 1 and 0.
These figures depict a variety of statistics. It is known as a binary or base 2 number system since just two digits
are needed to represent numbers.
The positional notation is used in the binary number system. However, in this instance, each digit is multiplied
by the correct power of two according to its placement.
For example, (101101)2 in decimal is:
= 1 x 2 5 + 0 x 24 + 1 x 23 +
1 x 22 + 0 x 21 + 1 x 20
= 1 x 32 + 0 x 16 + 1 x 8 +
1x4+0x2+1x1
= 32 + 8 + 4 + 1
= (45)10
In Decimal Number System, 0 to 9 are used to represent numbers in this system. It is also known as the base-
10 number system because it only requires 10 digits to represent a number. Place value, which is dependent
on a digit's position, assigns each digit a value. As we move from the right to the left in the number, the value
of the location increases by 10 times.
For example, the value of 786 is
= 7 x 102 + 8 x 101+ 6 x 100
= 700 + 80 + 6
=786
Decimal number is the most
used number system in
general terms.
The Octal Number System. When referring to numbers with an eight as base, the term "octal" is used. This
system uses digits 0 to 7 (i.e. 8 digits) to represent a number.
The octal numbers are significant and have many applications, particularly in computers and digital numbering
schemes.
The base-16 notation is used
to write or represent
numbers in the hexadecimal
system. Each digit position
represents a power of 16. As
the base is greater than 10,
the number system is
supplemented by letters.
Following are the
hexadecimal symbols: 0,1, 2,
3, 4, 5, 6, 7, 8, 9, A, B, C, D,
E, F.
