1.4 Data Types, Data Structures and Algorithms

1.4 Data Types, Data Structures and Algorithms


1.4.1 Data Types

Primitive Data Types:

 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.


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, 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



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