S3 CS - Data representation (revision)

S3 Data representation revision

BGE Computing Science - Falkirk High School

Binary

Machine language

Data on a computer is all stored in binary code. Binary code consists of 1's and 0's and can be used to store numbers, text, graphics, video and audi.

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Advantages of binary

• Calculations are kept simple

• Degraded data is still recognisable

• ​Simplicity involves in only having to detect two voltage levels

Converting Binary to Decimal

The problem

Convert the binary number 10110011 to decimal.

Draw a table with 8 columns and 2 rows. In the far right column place a 1 in the top row, double the number as you move right-left. Insert the binary number and count the numbers with a 1.

BGE Computing Science​ - Falkirk High School

​128	​64	​32	​16	​8	​4	​2	​1
​1	0​	​1	1​	​0	0​	​1	1​

128 + 32 + 16 + 2 + 1 = 179

Multiple Choice

Which of the following decimal numbers match with the binary number - 01101101

• 107

• 108

• 109

• 110

Multiple Choice

Which of the following decimal numbers match with the binary number - 11001111

• 207

• 208

• 209

• 210

Multiple Choice

Which of the following decimal numbers match with the binary number - 11101100

• 235

• 236

• 238

• 240

Multiple Choice

Which of the following numbers represents the highest decimal number which can be represented with 8 bits?

• 15

• 253

• 254

• 255

Converting Decimal to Binary

The problem

Convert the binary number 165 to decimal.

Draw a table with 8 columns and 2 rows. In the far right column place a 1 in the top row, double the number as you move right-left.

Move from left to right placing a 1 under each column that results in the number being less than or the same as the target number.​

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​128	​64	​32	​16	​8	​4	​2	​1
​1	​​0	​	​	​	​	​	​

128 + 64 = 192

Converting Decimal to Binary

The problem

BGE Computing Science​ - Falkirk High School

​128	​64	​32	​16	​8	​4	​2	​1
​1	​​0	​1	0​	​	​	​	​

128 + 32 + 16 = 176

Convert the binary number 165 to decimal.

128 + 32​ = 160

​128	​64	​32	​16	​8	​4	​2	​1
​1	​​0	​1	​	​	​	​	​

​128	​64	​32	​16	​8	​4	​2	​1
​1	​​0	​1	0​	0​	​	​	​

128 + 32 + 8 = 168

Converting Decimal to Binary

The problem

BGE Computing Science​ - Falkirk High School

​128	​64	​32	​16	​8	​4	​2	​1
​1	​​0	​1	0​	0	1​	0​	1​

128 + 32 + 4 + 2 = 166

Convert the binary number 165 to decimal.

128 + 32​ + 4 = 164

128 + 32 + 8 = 165

​128	​64	​32	​16	​8	​4	​2	​1
​1	​​0	​1	0​	0	1​	​

​128	​64	​32	​16	​8	​4	​2	​1
​1	​​0	​1	0​	0	1​	0​

Multiple Choice

Which of the following binary numbers match with the decimal number - 189

• 10111101

• 10111100

• 11011101

• 10101101

Multiple Choice

Which of the following binary numbers match with the decimal number - 150

• 10010010

• 10010100

• 10010111

• 10010110

ASCII

Representing text

ASCII stands for American Standard Code for Information Interchange. It is used to represent text in a computer system.

​

• ASCII uses 8 bits to represent each character.

• Control characters such as tab, delete and backspace are also represented. They cause an effect on-screen but do not produce a printed character. ​

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Multiple Choice

How many bits does ASCII use to represent a character?

• 7

• 8

• 1

• 16

Fill in the Blanks

Multiple Choice

Which of the following is an example of a control character?

• A

• 8

• Tab

• !

Graphics

Bit-mapped graphics

• Bit-mapped graphics are stored as a 2-D array of pixels. The number of pixels is known as the resolution.

• In a black and white image, we only need two states to be able to store the graphics information.

• As more colours are added to the picture, more bits must be used to store each pixel. 

• The number of bits used to store the colour information is known as the colour-depth.​

BGE Computing Science​ - Falkirk High School

Graphics

Vector graphics

• Vector graphics are made up of individual objects layered together to make a graphic.

• ​Each object has a set of attributes, such as line colour, line weight and coordinates, stored.

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Multiple Choice

Bit-map graphics tend to have large file sizes.

• TRUE

• FALSE

Multiple Choice

The file size of a vector graphic increases when more shapes are added to the image.

• TRUE

• FALSE

Multiple Choice

Bit-mapped graphics allow for individual shapes to be arranged in layers.

• TRUE

• FALSE