1.4.1 Data Types - Done

-Integer -Real/floating point -Character -String -Boolean

They are needed so the computer knows how to store, process and interpret data correctly so that only valid operations are performed on data.

A whole number

A decimal number

A single letter, digit or symbol

A sequence of characters

A data type with only 2 possible values – true or false

Numeric, text, image and sound

Through their use of the character sets ASCII and Unicode. Each character is given a unique binary code. Increasing the number of bits for each character increases the number of possible characters that can be stored

Positive denary numbers can be represented through binary. Negative binary numbers can be stored using Sign and Magnitude and Two’s Compliment. Floating point binary can be used to store decimal numbers.

Images are split into pixels. Each pixel is given a binary value which represents colour.

Analogue sound is sampled. A sample is a reading that is taken at a certain point and stored as a binary number.

Computers are made up of switches which have 2 states: on and off. This can be easily represented using binary as it also has 2 states that can represent on and off: 1 and 0.

The number is written the same as in regular binary, however the left-most bit has become a sign bit (no longer representing a weighted value, but instead a sign) with 1 representing a negative number and 0 for if the number is positive.

Negative numbers are represented starting from 11111111 as the denary value -1. Starting from the right-most digit, you write the binary number exactly how it would appear in regular binary, up to and including the first 1. From that point onwards, swap every 0 for a 1 and vice versa.

• Calculations are easier to perform • Two’s complement allows for a larger range of numbers to be stored • It has only one representative station for 0 • No additional hardware is required

1 - 1 = 0 1 - 0 = 1 0 - 0 = 0 0 - 1 = 1, make the next digit of 1 a 0 and the digit to the right of it a 2

Add the negative version of one number to the positive of the other number to get the two’s complement form of the result. [a - b = a + (-b)]

-Hexadecimal values are shorter than binary so 4 bits can be represented using one character -This means they are faster, and more reliable to write down and read

The mantissa of a floating point number holds the actual digits of the value and represents the precision of the number. It’s usually 5 bits long. The exponent controls the size of the number as it governs where the decimal point is positioned. It’s usually 3 bits long. The exponent is written in Sign and magnitude. The decimal point starts between the first and second digits. If the exponent is positive the decimal moves right, if it’s negative it moves left. Each digit after the decimal represents 1/2^n (with n increasing the lower the digit is).

• It allows for greater accuracy from the given number of bits. • The representation of each binary value is unique.

A floating point where the mantissa starts with 01 if positive or 10 if negative. The normal exponent should be the difference between where the decimal point would be based on the original exponent and where it is after normalisation (negative if the normalised is further right, positive if it’s further left)

By moving all the bits in a binary number left/right a set number of places. In a right shift, the right most bits should be discarded. In a left shift, the empty righthand bits should be filled with zeros.

A right shift divides the number by 2, a left shift multiplies the number by 2.