Data representation Revision Notes

What is 7-bit ASCII?

7-bit ASCII is a character encoding standard that uses a 7-bit binary code to represent 128 different characters. These characters include uppercase and lowercase English letters, numbers, punctuation marks, and control characters.

How 7-bit ASCII works

Each character is assigned a unique decimal value, which is then converted into its 7-bit binary equivalent. For instance, 'A' is 65 (decimal), which is 01000001 (binary). When a computer stores or transmits text, it uses these binary codes. Upon reception or display, the binary codes are converted back to their corresponding characters.

Limitations of 7-bit ASCII

With only 128 possible characters (2^7), 7-bit ASCII is limited. It primarily supports English characters and basic symbols. It cannot represent characters from other languages (like Cyrillic, Greek, or Chinese) or a wide range of specialised symbols. This limitation led to the development of more comprehensive encoding schemes.

Purpose of Character Encoding

The primary purpose of character encoding standards like ASCII is to ensure interoperability. It guarantees that text data can be uniformly stored, exchanged, and displayed across different computing systems without corruption or misinterpretation.

Pixels as Building Blocks

Bitmap images are made up of millions of tiny squares called pixels. Each pixel is a single point of colour in the image. The computer stores the colour information for every single pixel in a binary format, like a vast array of coloured dots.

Resolution and File Size

Resolution defines the total number of pixels in a bitmap image (width x height). A higher resolution image contains more pixels, resulting in finer detail and clearer visuals. However, more pixels mean more data to store, leading to a larger file size.

Colour Depth Explained

Colour depth determines the number of bits used to represent the colour of each individual pixel. More bits per pixel allow for a greater range of colours. For example, 1 bit offers 2 colours, 8 bits offer 256 colours, and 24 bits (True Colour) offer over 16 million colours. Higher colour depth increases image quality but also file size.

Binary Representation

All the data for pixels, including their colour information, is stored in binary. The combination of resolution and colour depth dictates the total amount of binary data required to represent the entire image, directly impacting its file size.

Sampling Analogue Sound

Analogue sound waves are continuous. To convert them to a digital format (binary), we must sample them. Sampling involves taking measurements of the sound wave's amplitude at regular intervals to create discrete data points.

Key Terminology in Digital Sound

Amplitude refers to the height or intensity of the sound wave at a given point. Sample rate is the number of samples taken per second, measured in Hertz (Hz). A higher sample rate captures more detail of the original wave. Bit depth determines the number of bits used to store the amplitude of each sample, defining the range of possible amplitude values. A greater bit depth results in a more accurate representation and higher fidelity. The sample interval is the time between consecutive samples, inversely related to the sample rate.

Impact of Sample Rate and Bit Depth

Increasing the sample rate captures more data points over time, allowing for a more accurate representation of the original waveform's frequency changes and reducing aliasing. Increasing the bit depth allows for a wider range of amplitude values to be recorded, making the digital sound closer to the original analogue sound's dynamic range and reducing quantisation error. Both factors contribute to higher sound quality but also result in larger file sizes.

Finite Bit Constraints

Computers use binary (0s and 1s) to represent all data. The number of bits available to represent a piece of data directly impacts the range of values and the precision with which that data can be stored. A fixed number of bits means a fixed capacity for data representation.

Integer Limitations: Overflow

When representing whole numbers (integers), a limited number of bits means there's a maximum positive and minimum negative value that can be stored. If a calculation produces a result larger than this maximum or smaller than this minimum, an 'overflow' error occurs, often leading to incorrect results or program crashes. For example, with 8 bits, the maximum unsigned integer value is 255. Any value greater than this cannot be represented.

Fractional Limitations: Rounding and Truncation

Decimal numbers (floating-point numbers) are also represented in binary. With a limited number of bits, not all fractional values can be represented exactly. This leads to 'rounding' errors, where the number is stored as the closest representable value, or 'truncation', where digits beyond the bit limit are simply cut off. For instance, 0.1 cannot be represented exactly in binary, no matter how many bits, similar to how 1/3 cannot be represented exactly in decimal.

Impact on Media Data

Digital media like images and audio are represented by discrete samples. Each sample's value is stored using a certain number of bits. If too few bits are used per sample (low bit depth), it results in 'quantisation errors'. In images, this can lead to 'colour banding' or a reduced colour palette. In audio, it can result in audible distortion or a lack of dynamic range, impacting the quality or 'fidelity' of the sound.