CHAPTER No. 1
Binary Systems and
Hexadecimal
, Binary Systems and Hexadecimal
1.1 Binary Number System
“Binary number system is a number system which contains only two digits 0 or 1”
In mathematics and digital electronics, a binary number is a number expressed in
the binary numeral system or base-2 numeral system which represents numeric values using
two different symbols: typically 0 (zero) and 1 (one).
The binary system is used internally by almost all modern computers and computer-
based devices. Each digit is referred to as a Binary Digit (bit).
1.1.1 Measurement of the size of computer memories
Following are the units used to measure the computer’s memory.
a) Bit
Bit stands for binary digit. A single binary digit can be a Zero or One. It is the smallest memory
unit.
b) Nibble
A group of 4 bits is called a nibble.
e.g. A = 1010
c) Byte
Group of 8 bits is called a byte.
1000 1101
It is the basic unit used for measurement of the memory.
It can be used to estimate the size of the memory (1 byte = 1 character or 1 Byte = 1 Pixel)
Bytes can be used to measure the size of bus width, word size, register size etc.
d) Large Units
Due to increasing storage capacity of secondary storage devices (hard disk) and primary
memory, we need larger units to measure the storage capacity of the devices. Some of the
commonly used memory units are illustrated in the given table.
Name of Memory Size Number of Bytes General Representation
1 Kilobyte (1KB) 210 bytes 1024 bytes
1 Megabyte (1MB) 220 bytes 1024 KB
1 Gigabyte (1GB) 230 bytes 1024 MB
1 Terabyte (1TB) 240 bytes 1024 GB
1 Petabyte (1PB) 250 bytes 1024 TB
Table 1.1 Memory Units
, 1.1.2 Example Use of Binary
a) Registers
“A register is a small group of bits. It is a small temporary storage area inside microprocessor.”
Register are used to control devices (such as robots), and to store data and instructions. All the
instructions and data that are currently being used by microprocessor is stored in register. This
data is stored in binary form.
b) Transistors
The circuits in a computer's processor are made up of billions of transistors. A transistor is a
tiny switch that is activated by the electronic signals it receives. The digits 1 and 0 used in
binary reflect the ON and OFF states of a transistor.
1.2 Hexadecimal System
Hexadecimal (also known as hex) is a base 16 number system and therefore
needs to use 16 different values to represent each digit. Hexadecimal number system includes
the number 0 to 9 and the letters A to F to represent each hex digit. (A=10, B=11, C=12, D=13,
E=14 and F=15).
1.2.1 Use of Hexadecimal System
a) Memory Dumps
Definition
“A memory dump is a process in which the contents of memory are displayed and
stored in case of an application or system crash. “
Memory dump helps software developers and system administrators to identify and resolve
the problem that led to application or system failure.
Use of Hex in Memory Dumps
Hexadecimal is used when developing new software or when programmer wants to
trace error in programs. Hexadecimal is preferred by the programmers because it is easy to
understand as compared to stream of 0’s and 1’s (binary number system).
Memory Addresses Contents of Memory
Fig. 1.1 Memory Dump
A program developer can look at each of the hexadecimal codes (as shown in the fig 1) and determine
where the error lies.
, b) Hyper Text Markup Language
Definition
Hyper Text Markup Language (HTML) is used for writing and developing web pages.
HTML is not a programming language but is simply a mark-up language. It is used to define
process and present the text.
HTML uses <tags > to bracket a piece of code. Basic structure of html code is as follows.
<html>
<head>
<title>My First Page</title>
</head>
<body>
Hello world!
</body>
</html>
Use of Hex in HTML
HTML code is often used to represent colours of the text on computer screen. The
different intensity of three primary colours can be used to produce almost any colour the user
wants. The following table shows the hexadecimal codes of different colours used in HTML.
Colour Name Hexadecimal Code
RED #FF0000
Green #00FF00
Blue #0000 FF
White #FFFFFF
Silver #C0C0C0
Grey #808080
Black #000000
Maroon #800000
Purple #800080
Table 1.2 Colour Codes in Hexadecimal
c) Media Access Control (MAC)
Definition
Media Access Control (MAC) address is a unique number used to identify the device on the
internet.
MAC addresses are most often assigned by the manufacturers.
MAC address is stored in its ROM or some other firmware mechanism.
Binary Systems and
Hexadecimal
, Binary Systems and Hexadecimal
1.1 Binary Number System
“Binary number system is a number system which contains only two digits 0 or 1”
In mathematics and digital electronics, a binary number is a number expressed in
the binary numeral system or base-2 numeral system which represents numeric values using
two different symbols: typically 0 (zero) and 1 (one).
The binary system is used internally by almost all modern computers and computer-
based devices. Each digit is referred to as a Binary Digit (bit).
1.1.1 Measurement of the size of computer memories
Following are the units used to measure the computer’s memory.
a) Bit
Bit stands for binary digit. A single binary digit can be a Zero or One. It is the smallest memory
unit.
b) Nibble
A group of 4 bits is called a nibble.
e.g. A = 1010
c) Byte
Group of 8 bits is called a byte.
1000 1101
It is the basic unit used for measurement of the memory.
It can be used to estimate the size of the memory (1 byte = 1 character or 1 Byte = 1 Pixel)
Bytes can be used to measure the size of bus width, word size, register size etc.
d) Large Units
Due to increasing storage capacity of secondary storage devices (hard disk) and primary
memory, we need larger units to measure the storage capacity of the devices. Some of the
commonly used memory units are illustrated in the given table.
Name of Memory Size Number of Bytes General Representation
1 Kilobyte (1KB) 210 bytes 1024 bytes
1 Megabyte (1MB) 220 bytes 1024 KB
1 Gigabyte (1GB) 230 bytes 1024 MB
1 Terabyte (1TB) 240 bytes 1024 GB
1 Petabyte (1PB) 250 bytes 1024 TB
Table 1.1 Memory Units
, 1.1.2 Example Use of Binary
a) Registers
“A register is a small group of bits. It is a small temporary storage area inside microprocessor.”
Register are used to control devices (such as robots), and to store data and instructions. All the
instructions and data that are currently being used by microprocessor is stored in register. This
data is stored in binary form.
b) Transistors
The circuits in a computer's processor are made up of billions of transistors. A transistor is a
tiny switch that is activated by the electronic signals it receives. The digits 1 and 0 used in
binary reflect the ON and OFF states of a transistor.
1.2 Hexadecimal System
Hexadecimal (also known as hex) is a base 16 number system and therefore
needs to use 16 different values to represent each digit. Hexadecimal number system includes
the number 0 to 9 and the letters A to F to represent each hex digit. (A=10, B=11, C=12, D=13,
E=14 and F=15).
1.2.1 Use of Hexadecimal System
a) Memory Dumps
Definition
“A memory dump is a process in which the contents of memory are displayed and
stored in case of an application or system crash. “
Memory dump helps software developers and system administrators to identify and resolve
the problem that led to application or system failure.
Use of Hex in Memory Dumps
Hexadecimal is used when developing new software or when programmer wants to
trace error in programs. Hexadecimal is preferred by the programmers because it is easy to
understand as compared to stream of 0’s and 1’s (binary number system).
Memory Addresses Contents of Memory
Fig. 1.1 Memory Dump
A program developer can look at each of the hexadecimal codes (as shown in the fig 1) and determine
where the error lies.
, b) Hyper Text Markup Language
Definition
Hyper Text Markup Language (HTML) is used for writing and developing web pages.
HTML is not a programming language but is simply a mark-up language. It is used to define
process and present the text.
HTML uses <tags > to bracket a piece of code. Basic structure of html code is as follows.
<html>
<head>
<title>My First Page</title>
</head>
<body>
Hello world!
</body>
</html>
Use of Hex in HTML
HTML code is often used to represent colours of the text on computer screen. The
different intensity of three primary colours can be used to produce almost any colour the user
wants. The following table shows the hexadecimal codes of different colours used in HTML.
Colour Name Hexadecimal Code
RED #FF0000
Green #00FF00
Blue #0000 FF
White #FFFFFF
Silver #C0C0C0
Grey #808080
Black #000000
Maroon #800000
Purple #800080
Table 1.2 Colour Codes in Hexadecimal
c) Media Access Control (MAC)
Definition
Media Access Control (MAC) address is a unique number used to identify the device on the
internet.
MAC addresses are most often assigned by the manufacturers.
MAC address is stored in its ROM or some other firmware mechanism.
