Cambridge International AS and A Level Computer Science Coursebook
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Topical Lecture A level notes , Cambridge International AS and A Level Computer Science (9806)
CIE AS Computer Science Paper 1 notes
Cambridge Computer Science Paper 1 notes and common questions. Seal your high grade today!
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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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