4.5 Fundamentals of data representation

• Sound synthesis produces smaller file sizes without loss of quality • Sound synthesis allows for easy editing of files after they have been recorded • Sound synthesis allows for sounds that would be unachievable using traditional instuments

• Sound synthesis struggles to recreate the sounds made by traditional instruments • Sound synthesis struggles to recreate the human voice

Musical Instrument Digital Interface

List of Event Messages that explain what notes must be played, when they must played, and how long or loud each note should be.

• Digital signals that specify notation, pitch, and intensity • Control signals for parameters such as volume and vibrato • Clock signals to set the tempo

Base 10

Representing large numbers since you need fewer digits. 2 hex digits = 1 byte i.e. Representing colours

When you have binary with a decimal point that can “float” meaning that it can be placed anywhere in the number.

Binary where you have a decimal point in a fixed place, and fractional parts to the right of the point

Base 2, meaning it only uses 2 characters, 0 and 1, known as bits

A nibble

Cancellation : Adding a very small number to a very large number will not change the result Underflow : The result of a calculation is too small to fit into the available number of bits Overflow : The result of a calculation is too big to fit into the available number of bits. Rounding : Some number just can’t be represented using binary. Rounding errors can be represented in absolute, relative and percentage forms

Since we can never accurately represent some fractional numbers in binary (for instance 1/3), we often must accept a certain amount of inaccuracy. However, it is possible to change the position of the binary point to alter the balance between range and accuracy

256

Convert the number you’re subtracting into two’s compliment and then add the two numbers

B^n Where B is the number base and n is the number of digits

16^2 16^1 16^0 Use those headings, convert each hex digit to denary and then multiply by its heading. Total each of the values you get at the end.

Convert each of the hexideciamal digits to denary seperately then convert each denary value into 4 bit unsigned binary and then just put the binary together

• Work out the value of the exponent • Denormalise the mantissa (using the exponent) – Moving the the point • Calculate the denary value as normal

• Convert denary to fixed point binary • Normalise the number • Check what exponent you need to get back to the original number • Convert the exponent to binary • Put the mantissa and the exponent together, making sure you use the correct number of bits for each number

Split the binary into sections of 4 bits and convert each of them to denary, then convert to denary values to Hex values and just put them together

When the most significant bit in binary is negative, allowing you to represent negative numbers with binary

The first two bits are different from each other

Mixes Two’s Complement and fixed point binary by having the most significant bit be negative whilst also having numbers after a decimal point.