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define the terms bit, nibble, byte, kilobyte,
megabyte, gigabyte, terabyte
understand that data needs to be converted
into a binary format to be processed by a
computer
bit
nibble
byte
kilobyte
megabyte
gigabyte
terabyte
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convert positive denary whole numbers (0-255)
into 8-bit binary numbers and vice versa
add two 8-bit binary integers and explain
overflow errors which may occur
convert positive denary whole numbers (0-255)
into 2-digit hexadecimal numbers and vice
versa
convert between binary and hexadecimal
equivalents of the same number
explain the use of hexadecimal numbers to
represent binary numbers.
Can you say what the
time is?
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In denary (base 10) there are 10 different
symbols used to write numbers 0, 1, 2, 3, 4,
5, 6, 7, 8, 9.
Numbers can be written in a table where each
column to the left is 10 times the one on the
right
100s
10s
Units
2
3
4
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In binary (base 2) there are only two symbols
0, 1. In the binary table, each column is twice
that on its right
128
64
32
16
8
4
2
1
1
1
1
0
1
0
1
0
128+64+32+0+8+0+2+0 = 234
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Convert these numbers into denary
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◦
◦
◦
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00001111
00101010
00101101
11100010
00010001
11101110
01010101
128
64
32
16
8
4
2
1
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Convert these numbers into binary
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◦
◦
◦
◦
◦
◦
◦
6
15
39
54
106
180
200
249
128
64
32
16
8
4
2
1
128
1
0
64
0
0
32
1
1
16
1
1
8
0
1
4
0
0
2
1
1
Complete the additions on the sheet
1
0
1
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In hexadecimal (base 16) there are 16
symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D,
E, F. In the hexadecimal table, each column
is 16 times that on its right
256
16
1
0
E
A
(16*E) + 10 = (16*14) + 10 = 224 + 10
Denary
Hex
0
0
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
A
11
B
12
C
13
D
14
E
15
F
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Because it isn’t obvious that 20 is in base 16
it is sometimes written as (20)16
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Find how many times 16 will fit into the
number (remembering that you can go up to
15)
180 / 16 = 11 r 4
16
1
B
4
So 180 = B4 in base 16
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Convert these numbers into hexadecimal
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233
21
9
75
188
56
4
121
16
1
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Convert these numbers into denary
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(5A)16
(CC)16
(97)16
(40)16
(07)16
(3D)16
(FB)16
(E4)16
16
1
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Split the binary number into 2 nibbles
Find the hex for each nibble
1
1
1
0
8
4
2
1
8
4
2
1
1
1
1
0
1
0
1
0
16
1
E
A
= E (14 in denary)
1
0
1
0
=A (10 in denary)
= 14*16 + 10*1 = 234
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Convert these numbers into Binary
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(45)16
(FA)16
(5D)16
(99)16
(03)16
(6B)16
(DD)16
(FE)16
8
4
2
1
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Convert these numbers into Hex
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11001100
11110001
00110001
11000010
10100100
10100111
11101100
11111100
8
4
2
1
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explain the use of binary codes to represent
characters
explain the term "character set"
describe with examples (e.g. ASCII and
Unicode) the relationship between the
number of bits per character in a character
set and the number of characters which can
be represented
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Every time a character is typed on a keyboard a
code number is transmitted to the computer
The code numbers are stored in binary
Different sets of codes are available for different
types of computer
PCs use a character set called ASCII
The simplest form of ACII uses 7-bit encoding
(72 or 128 different codes)
Unicode uses 16-bit encoding (162 or 65,536
different codes)
EBCDIC uses 8-bit character encoding (82 or 255
different codes)
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explain the representation of a image as a
series of pixels represented in binary
explain the need for metadata to be included
with the file such as height, width and colour
depth
discuss the effect of colour depth and
resolution on the size of an image file
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A vector graphic is made up of lines whith
specific properties such as line style, line
colour and where it starts and ends. The
computer sores all of this data in binary.
A bitmap graphic is made up of information
about each pixel in the image
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The number of pixels per inch (usually known
as dots per inch or dpi) is known as the
resolution of the picture. The more dots per
inch the better the resolution but the larger
the file.
The number of bits used to store each pixel
dictates how many colours the picture can
contain, for example 8 bits per pixel will give
256 colours. This is known as the colour
depth. Again the more bits per pixel, the
bigger the file.
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An image file is just a series of binary
numbers
010101110011110001110000111….. Etc.
In order for the computer to interpret the file
and display the image it must know extra
information such as the resolution of the file
(i.e. the height and width of the picture e.g.
600x800) and the colour depth. This
information is called metadata – and is stored
in the file itself in binary
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explain how sound can be sampled and
stored in digital form
explain how sampling intervals and other
considerations affect the size of a sound file
and quality of its playback.
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Take a strip of questions and ask your
partner, then swap and ask the other way.
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explain how instructions are coded as bit
patterns
explain how the computer distinguishes
between instructions and data.
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Computer programs are made up of
instructions written in a programming
language. When a program is compiled, the
computer turns the high level programming
language into machine code, which is the
binary representation of the instructions.
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Data and instructions are both in binary (von
Neuman architecture) so the operating
system has to know which is which. Every
location in memory has a unique address
(location number) and the operating system
knows where in memory the data is stored
and where the programs are stored.
Answer the past paper questions to do with
representing data in computer systems
Computing/past papers/past paper questions
by topic/DataRepresentation
 Check your answers using the answer sheet
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