BINARY NUMBERS

• Any digital data has a numerical representation using binary numbers.

• A bit is the smallest unit of information stored or manipulated on a computer; it consists of either zero or one.

Base Conversion

Binary to Decimal Conversion

• Of course, binary numbers are rarely used in real life.

• Therefore, programmers must be able to go back and forth between the binary numbers we use in computing and the decimal numbers that we use in everyday life.

• The key is to remember that the different binary digits represent different powers of 2.

• For example, let's use the binary number 1101.

Decimal to Binary Conversion

• We need to find the powers of 2 that add up to the given decimal number. Start by finding the largest power of 2 that is less than the number.

• Subtract that number from the original, and repeat until you're down to 0.

• Try the example of the decimal number 200.

Digital Images as Bits

• Images displayed on the screen are converted into binary formats and then processed by a computer displayed on our screen.

• Digital images: are a collection of pixels. where each pixel consists of binary numbers.

• If we say that one is black (or on) and o is white (or off), then a simple black and white picture can be created using binary Draw a grid and color the squares (1-black and 0-white) to create the picture

• However, before creating the grid, the site of the grid needs to be known.

  • This data is called metadata, and computers need metadata to know the size of an image.

  • The metadata for the image to be created is 10 x 10; this means the picture will be 10 pixels across and 10 pixels down.

Binary and Color Representation

• Images: are not often just black and white.

• To represent colors computers also use binary numbers.

• Color: is based on light.

• Any color can be created using red, green and blue light.

• The maximum value for any color in decimal 255, which is repte sented by 11111111 in binary.

• The minimum number is 0.

Music as Bits

• An analog signal exists throughout a continuous interval of time and takes on a continuous range of values.

• A digital signal is a sequence of discrete symbols.

  • If these symbols are zeros and ones, we call them hits.

  • As such, a digital signal is neither continuous in time nor continuous in its range of values.

• Sampling: is recording an analog signal at regular discrete moments and converting them to a digital signal.

• Digital signals are resilient against noise.

DATA COMPRESSION

• Data compression: is used everywhere.

• Mp3, mp4, rar, zip, jpg, and png files (along with many others) all use compressed data.

• Compression: is also an important consideration when it comes to backing up and archiving your important files, particularly for uploading over the Internet.

  • Compression is a two- way process: a compression algorithm can be used to make a data package smaller, but it can also run the other way, to decompress the package into its original form.

• Data compression: is useful in computing to save disk space, or to reduce the bandwidth used when sending data (eg, over the Internet).

• Data compression deals with taking a string of bytes and compressing it down to a smaller set of bytes, whereby it takes either less bandwidth to transmit the string or to store it to disk.

• Lossless algorithms: are those that can reconstruct the original message exactly from the compresed message, and lossy algorithms can only reconstruct an appsimation of the original message.

  • Lossless algorithms are typically used for text, and lowy algorithms for images and sound where a little bit of loss in resolution is often undetectable, or at least acceptable.

• Lossless compression: packs data in such a way that the compressed package can be decompressed, and the data can be pulled out exactly the same as it went in.

• Text compression: is another important area for lossless compression.

  • It is very important that the reconstruction is identical to the original text, as very small differences can result in statements with very different meanings.

• Lossy compression is a technique that does not decompress digital data back to 100% of the original.

  • Lossy methods can provide high degrees of compression and result in smaller compressed files, but some number of the original pixels, sound waves, or video frames are removed forever.

  • Lossy is used in an abstract sense, however, and does not mean random lost pixels, but instead means loss of a quantity such as a frequency component, or perhaps loss of noise.

• Images: high image compression loss can be observed in photos when enlarged

• Music: there is a difference between an MP3 music and a high-resolution audio file

• Video: moving frames of video can handle a greater loss of pixels compared to an image

USING PROGRAMS WITH DATA

• The increase in digitization of information, mixed with multiple transactions, has resulted in a flood of data.

• The advancement in technology has promoted the rapid growth of data volume in recent years.

• By analyzing large data sets of data, it is possible to categorize connections from unconnected data sources and find specific patterns.

• Data extraction: is the process of obtaining data from a database or software such as a social media website so that it can transport it to another software (such as spreadsheets) designed to support online analytical processing.

• Data extraction is the first step.

  • The next step is to transform (either through filters or programs).

  • The final step is to analyze using graphs and other data visualization tools.

Below are the steps to extract data and analyze them:

• Analyze the data sources.

  • Data sources are found in different forms like web pages, emails, and chat video files, audio files, text documents, customer messages.

• Know what will be done with the results of the analysis.

  • It is vital to understand what sort of outcome is required.

  • Is it a trend, effect, cause, quantity, or something else that is needed?

• Decide the tools needed to read the data, and the repositories such as databases needed to store the data.

  • Clean the data of whitespace, symbols, duplicates, etc.

  • Understand the data patterns and text flow. This should be done using visualization tools.

How to read and analyze graphs

• A graph is a pictorial representation, a diagram used to represent data.

  • It usually is used to depict a relationship.

  • Graphs and charts: represent data in points, lines, bars, pie charts, and scatter plots.

  • Different types of graphs and charts display data in different ways.

  • Some are better suited than others for different uses.

• Picture graphs: use pictures to represent values.

• Bar graphs: use either vertical or horizontal bars to represent the values.

• Line graphs: use lines to represent the values.

• Scatter plots: represent the data with points, and then a best-fit line is drawn through some of the points.

Chapter 3: Algorithms and Programming