This is the topic: 1.4 Data Types, Data Structures and Algorithms for the OCR A-Level Computer Science (H446) course.
I got 4 A*s in my A-Levels (Computer Science, Physics, Maths, Further Maths) , so they are very detailed and cover all of the specification for this topic.
Integer: Whole number (e.g. 2, 0, -5)
Real: Any number with decimal places (e.g. 2.00, 5.83)
Boolean: Restricted to True or False
Character: A single symbol used by a computer
String: A collection of characters (can be a single character)
Positive Binary Integers:
Bit = A single binary digit. Eight bits are a byte. Four bits is a nibble.
Least significant bit = Furthest to the right.
Most significant bit = Furthest to the left.
A bit is 0 or 1. Having two states makes it simpler to build electronic devices. A binary number can
have a variety of different interpretations depending on what is being stored (e.g. numeric, text,
image, sound).
With positive integers, we can represent them in binary as usual.
(E.g.) 8 Bits:
128 64 32 16 8 4 2 1
Negative Binary Integers:
We can represent negative numbers in binary several ways:
Sign and Magnitude
Two’s Complement
Sign and Magnitude:
Positive numbers start with a zero, negative
numbers start with a 1.
Nothing else changes.
The most significant bit has become a ‘sign bit’, so it doesn’t represent an actual value.
Therefore, 8 bit numbers can only hold 7 bit values (but we now store -127 to 127).
Two’s Complement:
Positive numbers start with a zero, negative numbers
start with a 1.
The most significant bit is the negative of that value (e.g.
8 bits: -128).
We can find the two’s complement of a number by calculating using the negative MSB or by
the simple method.
Simple method:
o Write out positive version of number
o Invert all the bits (i.e. 1s become 0s and vice versa)
o Add one.
1
, Binary Addition and Subtraction:
Addition:
Because binary is base 2,
when we get 1 + 1, it
becomes 0 again and we
carry the 1.
Example: “95 + 222”
Here we have an overflow as we’re let with a 1 we need to carry.
We need an extra bit if there’s an overflow error.
Subtraction:
To subtract, we convert the number to subtract into two’s complement, then we add them.
Both numbers (to begin with) must be signed (i.e. 0 or 1 at start).
Hexadecimal:
Hexadecimal is base 16. The characters 0-9 are
normal, and the characters A-F represent 10-15.
Places start with 1 and go up in powers of 16.
It’s useful to represent large binary numbers in a
smaller number of digits.
They’re used to represent colours, MAC addresses, memory addresses, and more.
Hexadecimal to Binary:
Convert the hexadecimal digits into their decimal numbers (e.g. 9 = 9, B = 11)
Convert each of these into a binary nibble.
Combine the nibbles to form a single binary number.
Hexadecimal to Denary:
Convert the hexadecimal number into binary, then convert this into a denary number.
Alternatively, use the place values of hexadecimal (1, 16, 256…).
Floating-Point Binary:
To store fractional numbers in binary, we extend the number line from left to right. The
place values halve as we move from left to right (e.g. ½, ¼, 1/8) and we place a binary point
between the 1 and 1/2.
The number line begins with a negative value (e.g. -16)
Fixed Point Binary: The position of the point is fixed on the number line and the range of numbers
we can store is limited, and some numbers can’t be stored accurately (e.g. 1/3).
Positive: = 3.75
Negative: = -6.5
2
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller maddysunter1. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for £2.99. You're not tied to anything after your purchase.
