Cambridge International AS and A Level Computer Science Coursebook
Unlock the Power of Data: From Bits to Bytes!
Are You Ready to Dive Into the World of Data Representation?
Whether you're working with numbers, images, sound, or graphics, understanding how data is represented is crucial for success in today's digital world. Explore how systems like Binary,...
Topical Lecture A level notes , Cambridge International AS and A Level Computer Science (9806)
CIE AS Computer Science Paper 1 notes
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Information Representation
Data Representation
The two fundamental characteristics of any number system
are:
A base: The number of different digits that a system can use
to represent numbers
Place value: The specific-value of a digit based on its
position within a number
Denary - Base 10
Binary Systems - Base 2
Possible bits (binary digits): 0 and 1
12 6 3 1
8 4 2 1
8 4 2 6
0 0 0 0 0 0 0 0
Binary Coded Decimal (BCD)
Binary representation where each positive denary digit is
represented by a sequence of 4 bits (nibble).
Only certain digits are converted to BCD because particular
digits represent a digit greater than 9.
For example, to represent 429 in BCD:
1. Convert each individual digit of the number to its binary
equivalents -
2. 4 = 0100
3. 2 = 0010
4. 9 = 1001
, 5. Concatenate the 3 nibbles (4-bit group) in order to
produce BCD: 0100 0010 1001
Practical applications:
A string of digits on any electronic device displaying
numbers (like in calculators)
Accurately measuring decimal fractions
Electronically coding denary numbers
Two’s Complement
We can represent a negative number in binary by making the
most significant bit (MSB) a sign bit, which indicates whether the
number is positive or negative.
● Converting from negative denary to binary two’s
complement (example -42):
1. Find the binary equivalent of the denary number (ignoring
the negative sign) | 42 = 101010
2. Add extra 0 bits before the MSB, to format the binary
number to 8 bits | 00101010
3. Convert binary number to one’s complement (flip the bits) |
11010101
4. Convert binary number to two’s complement (add 1) |
1010101 + 1 = 11010110
● Converting binary two’s complement into denary
(example 11010110):
1. Flip all the bits | 00101001
2. Add 1 | 00101010
3. Convert binary to denary and put a negative sign) | -42
4. Maximum positive number in 8 bits: 127
5. Maximum negative number in 8 bits: -128
Hexadecimal Systems - Base 16
● Possible digits: 0 to 9 and A to F, where A to F represent
denary digits 10 to 15
● Practical applications:
1. Defining colours in HTML
2. Defining Media Access Control (MAC) addresses
3. Assembly languages and machine code
4. Debugging via memory dumps
5. Example - A5 in Denary = (16×10) + (1×5) = 165
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