IGCSE Hodder Computer Chapter 1 Data Representation

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Chapter 1 Data Representation

​The binary number system is a base 2 number system. It is based on the number 2. Thus, only the two ‘values’ 0 and 1 can be used in this system to represent all

​

​What is Binary system?

​Converting from binary to denary

The conversion from binary to denary is a relatively straightforward process. Each time a 1-value appears in a binary number column, the column value (heading) is added to a total.​

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​Examples of conversion from binary to denary:

​Another Example

Multiple Choice

Which topic did we studied about?

• Binary System

• Hexadecimal

• Data storage and Compression

• 8-bit numbers

Multiple Choice

​The binary number system is a base 2 number system. It is based on the number 10.

• True

• False

Multiple Choice

Only the one value can be used in this system to represent it.

• True

• False

Multiple Choice

The conversion from binary to denary is a relatively _________ process

• Complicated

• Validation

• straightforward

• step-by-step approch

Multiple Choice

Each time a 1 appears in a column, the column value is added to the ______

• Base

• Digits

• Total

• 0

​Converting from denary to binary

The conversion from denary numbers to binary numbers can be done in two different ways. The first method involves successive subtraction of powers of 2 (that is, 128, 64, 32, 16, and so on); whilst the second method involves successive division by 2 until the value “0” is reached.​

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​Example 1 Method 1

​Example 1 Method 2

​Example 2 Method 1

​Example 2 Method 2

​Example 3 Method 1

​Example 3 Method 2

Hexadecimal

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The hexadecimal number system is very closely related to the binary system. Hexadecimal (sometimes referred to as simply ‘hex’) is a base 16 system and therefore needs to use 16 different ‘digits’ to represent each value. Because it is a system based on 16 different digits, the numbers 0 to 9 and the letters A to F are used to represent each hexadecimal (hex) digit. A in hex = 10 in denary, B = 11, C = 12, D = 13, E = 14 and F = 15.​

​Uses of the hexadecimal system

• ​Error Codes

• MAC Addresses​

• IPv6​ Addresses

• HTML Color Codes​

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​Error codes

Error codes are often shown as hexadecimal values. These numbers refer to the

memory location of the error and are usually automatically generated by the

computer. The programmer needs to know how to interpret the hexadecimal error

codes.​

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Mac Addresses

Media Access Control (MAC) address refers to a number which uniquely identifies

a device on a network. The MAC address refers to the network interface card (NIC)

which is part of the device. The MAC address is rarely changed so that a particular

device can always be identified no matter where it is. A MAC address is usually made up of 48 bits which are shown as 6 groups of two hexadecimal digits (although 64-bit addresses also exist)​

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Internet Protocol (IP) addresses

Each device connected to a network is given an address known as the Internet

Protocol (IP) address. An IPv4 address is a 32-bit number written in denary or

hexadecimal form: e.g. 109.108.158.1 (or 77.76.9e.01 in hex). IPv4 has recently

been improved upon by the adoption of IPv6. An IPv6 address is a 128-bit

number broken down into 16-bit chunks, represented by a hexadecimal number.​

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HyperText Mark-up Language (HTML) colour codes

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HyperText Mark-up Language (HTML) is used when writing and developing webpages. HTML isn’t a programming language but is simply a mark-up language. A mark-up language is used in the processing, definition and presentation of text (for example, specifying the colour of the text).​ HTML is often used to represent colours of text on the computer screen. All colours can be made up of different combinations of the three primary colours (red, green and blue). The different intensity of each colour (red, green and blue) is determined by its hexadecimal value. This means different hexadecimal values represent different colours.​

Multiple Choice

Which one binary digit has a position value?

• 1, 16, 256

• 2, 4, 16, 32, 64, 128

• 1, 2, 4, 8, 16, 32, 64, 128

• 1, 2, 4, 16, 32, 64, 128

Multiple Choice

How many bytes are in a kilobyte?

• 1024

• 100

• 1234

• 128

Multiple Choice

Convert 129 to binary

• 10000001

• 01111110

• 01000000

• 11001100

Multiple Choice

What is 19 in hexadecimal

• 13
• 10011
• 19
• 1A

Multiple Choice

What is 27 in hexadecimal

• 1B
• 17
• 11011
• 1C

Multiple Choice

What is the maximum number of values that can be represented in 7 bits? (4-6)

• 16
• 256
• 65,536
• 128

Multiple Choice

What digits are part of the binary number system?

• 0-9

• 0-F

• 0 and 1

• 1-9

Multiple Choice

In a number system like binary, what is the value of each digit called?

• Place value

• Base

• Bargain value

• ASDA value

Multiple Choice

What number do you carry when adding two binary numbers?

• 0

• 1

• You never carry a number as numbers are heavy

Multiple Choice

Convert the binary number 1001 to decimal.

• 4

• 5

• 9

• 11

Multiple Choice

Convert the binary number 1110 to decimal.

• 3

• 10

• 15

• 14

Multiple Choice

Convert the binary number 1010 to decimal.

• 8

• 10

• 9

• 7

Multiple Choice

Add the binary numbers 01101101 and 11011011

• 0101001000

• 1010110111

• 1101010101

• 0110100101

Multiple Choice

What can a bit hold?

• 1 and 0

• 1 or 0

Multiple Choice

How many bits are in a nibble?

• 8

• 4

• 2

• 10

Multiple Choice

Each device connected to a network is given an address known as the?

• Domain Address

• Internet

  Protocol (IP) address

• MAC Address

• Internet Service Protocol (ISP)

Multiple Choice

An IPv4 address is a 35-bit number written in denary or

hexadecimal form

• False

• True