Computer Science, Broadly

We intend this book as an introduction to computer science, with a focus on creating problem solutions in the C# programming language. We should not jump in too quickly. You can get lost in our details and miss an idea of the much larger breadth of computer science.

Information Processing

Computer Science is the study and practice of information processing. This can take many forms. Many forms appear in electronic computers, but information processing takes place in many other contexts, too:

In the early days of electronic computers, the information was largely numerical, calculating mathematical functions.

Later analyzing textual information has become much more important, for instance: What can you tell about the severity of the current flu outbreak by analyzing the phrasing in Google searches?

Images are analyzed: What can a satellite image tell you about the distribution of drought?

Sounds: how do you convert verbal speech accurately into written sentences?

DNA holds information that our bodies process into proteins.

Our brain chemicals and electronic signals process information. There is rich interplay between cognitive scientists and computer scientists modeling problem solving in the brain with neural nets on a computer, sometimes to better understand brains and sometimes to better solve problems on an electronic computer.

Economic systems are becoming better understood in terms of the flow of information.

The computer doing computations and processing can be a familiar electronic computer, but it can be genes or brain chemicals, or a whole society as its economy adapts.


Algorithms are at the heart of traditional problem solving . An algorithm is a clearly expressed sequence of steps leading to a result in a finite amount of time.

A recipe for baking a pound cake is an algorithm.

Such an algorithm has useful concepts that we use later in computer programming:

  • A named sub-problem: your recipe may include the instruction “Beat 4 eggs.” The recipe probably says no more about it, but this is shorthand, a name for a simpler sequence of steps, an algorithm like:

    Beating Any Number of Eggs
    1. Get a bowl large enough for the eggs.
    2. For each egg:
       a. Crack its shell on the edge of the bowl.
       b. Add the contents of the shell to the bowl.
    3. Mix the eggs with a whisk.
    4. Continue with step 3 until you cannot
       distinguish the white and yolks.
  • Parameters: The egg beating instructions work, in general, for any number of eggs. To use these instructions for a particular pound cake, you must supply a specific value to use to make the general instructions become clear. The pound cake recipe that uses the egg beating instructions, uses the number 4 as the actual data.

  • Repetition: The instructions for cracking an egg are not written repeatedly, for every egg. The instruction is stated once, and we are told how long to go on: for each egg in step 2. Step 4 says when to stop repeating step 3.

Data Representation

A recipe represents data by words that get processed by a human reader. Machines have used different representations. One of the earliest adding machines, the Pascaline,’s_calculator, represented numbers by the angle of rotation of interlocked gears. An abacus uses the positions of groups of sliding beads to represent digits. The Jacquard loom,, used cards with each row of holes punched in them indicating which warp threads are raised and which lowered when a cross thread is woven in.

In modern electronic computers the most basic bit of data (actually called a bit) is held by two-state switches, often in the form of a higher voltage vs. a grounded state. The symbolic representation is often 0 vs. 1. This symbolism comes from the representation of integers in binary notation, also called base 2: It is a place value system, but where each place in a numeral is a 0 or a 1 and represents a power of two, so 1101 in binary can be viewed in our decimal system as \((1)2^3+(1)2^2+(0)2^1+(1)2^0=8+4+0+1=13\).

Computer hardware can only handle a limited number of bits at a time, and memory space is limited, so usually integers are stored in a limited space, like 8, 16, 32 or 64 bits. We illustrate with the smallest, 8 bits, called a byte. Since each bit has two possible states, 8 bits have \(2^8=256\) possible states. Directly considered as binary numerals, they represent 0 through \(2^8-1=255\).

We also want to represent negative numbers, and have about half of the available codes for them. An 8-bit signed integer in twos complement notation represents 0 through \(2^7-1\) just as the unsigned numbers do. These are all the 8-bit codes with a leading 0. A negative number \(n\) in the range \(-2^7=-128\) through -1, is represented by what would be the unsigned notation for \(n+2^8\). These will be all the 8-bit codes with a leading 1. For example -3 is represented like unsigned 256 - 3 = 253: 11111101 in binary.

Limited precision approximation of real numbers are stored in something like scientific notation, except in binary, roughly \(\pm(m)2^e\), with a sign, mantissa m and exponent e. Both e and m have fixed numbers of bits, so the limited options for the mantissa restricts the precision of the numbers, and the limited options for the exponent restricts the range. Data on these limits for different sized numeric codes is in Value Types and Conversions.

Once you have numbers, all sorts of other kinds of data can be encoded: Characters like on your keyboard each have a numerical code associated with each one. For example the unicode for the letter A is 65. Images are often represented as a sequence of colored pixels. Since the human eye is only sensitive to three specific colors, red, green, and blue, a pixel is represented by a numerical intensity for each of the three colors.

Instruction Representation

Besides the data, instructions need a representation too, and an agent to interpret them. In the earliest electronic computers the two-state switches were relays or later vacuum tubes, and the machine was manually rewired when a new set of instructions/program was needed. It was a great advance in the 1940’s when the instructions also became symbolic, represented by binary codes that the computer could recognize and act on, This code is called machine language. With machine language the instructions became a form of data that could be stored in computer memory. We distinguish the hardware on which programs are run from the stored programs, the software. The architecture of the hardware determines the form and capacities of the machine language, so machines with a different hardware architecture are likely to have distinct machine languages.

Biologists have a fair idea of how protein sequence data is encoded in DNA, but they are still working on how the DNA instructions are encoded controlling which proteins should be made when.

In this book we will not be writing instructions shown as sequences of 0’s and 1’s! Some of the earliest programs were to help programmers work with more human-friendly tools, and an early one was an assembler, a program that took easier to understand instructions and automatically translated them into machine language. An example assembler instruction would be like

MOV 13, X

to move the value 13 to a storage location identified by the name X.

Machine instructions are very elementary, so programming was still tedious, and code could not be reused on a machine with a different architecture.

The next big step past assembler was the advent of high level languages, with instructions more like normal mathematical or English expressions. Examples are Fortran (1954) and Cobol (1959). A Fortran statement for calculating a slope like


might require seven or or more machine code instructions.

To use a Fortran program required three steps: write it (onto punch cards originally), compile it to machine code, and execute the machine code. The compiler would still be architecture specific, but the compiler for an architecture would only need to be written once, and then any number of programs could be compiled and run.

A later variant for executing a high-level language is an interpreter. An interpreter translates the high-level language into machine code, and immediately executes it, not storing the machine code for later use, so every time a statement in the code is executed again, the translation needs to be redone. Interpreters are also machine-specific.

Some later languages like Java and C# use a hybrid approach: A compiler, that can run on any machine, does most of the work by translating the high-level language program into a low-level virtual machine language called a bytecode. This is not the machine language for any real machine, but the bytecode is simple enough that writing an interpreter for it is very easy. Again the interpreter for the bytecode must be machine-specific. In this approach:

Program source => COMPILER => bytecode => INTERPRETER => execution

Program Development Cycle

The easiest way to check your understanding of small new pieces of C# is to write a highly specified small program that will be sure to test the new ideas. That is totally unlike the real world of programming. Here is a more realistic sequence:

  1. Clients have a problem that they want solved.

  2. They connect with software developers.

  3. The clients discuss the needs of their users.

  4. The software developers work with them to make sure they understand the desired deliverables, and work through the design decisions and their tradeoffs.

  5. Software developers start building and testing and showing off the core pieces of the software, and build on out.

  6. The clients may not have a full idea of what they want and the software developers may not have a full idea of what is feasible, and seeing the latest version leads both sides to have a clearer vision. Then the previous process steps are repeated, iteratively refining the product.

  7. After a production version is out, there may be later versions and error fixes, again cycling back to the earlier steps.

Note that very important parts of this process are not centered on coding, but on communicating clearly with a possibly non-technical client. Communication skills are critical.

Key Computer Science Areas

Most of the introduction so far has been about key concepts that underlie basic programming. Most of the parts so far about electronic computers could have been written decades ago. Much has emerged since then,

  • the Internet

  • the development of economical multi-processor machines distributing computation into many parallel parts

  • the massive explosion of the amount of information to be stored from diverse parts of life

  • the coming Internet of things, where sensors are coming to all sorts of previously “dumb” parts of the world, that now can be tracked by GPS and reacted to in real time.

  • Computers are now embedded in all sorts of devices: toasters, thermostats,…. Automobiles of today have more computing power embedded in various devices than early mainframe computers.

We conclude with a brief discussion of some of the other organizing principles of computer science.


As the world is criss-crossed with media transmitting gigabytes of data per second, how do we keep the communication reliable and secure?


With multiple networked entities, how do we enhance cooperation, so more work is done in parallel?


As the amount of data stored skyrockets, how do we effectively store and efficiently retrieve information?


How do we predict the performance and plan the necessary capacity for computer systems? The most spectacular recent public failure in this area was the rollout of the federal Affordable Care website.


How do we design better/faster/cheaper/reliable hardware and software systems? What new programming languages will be more expressive, lead to fewer time-consuming errors, or be useful in proving that a major program never makes a mistake? Errors in programs controlling machines delivering radiation for cancer treatment have had errors and led to patient death.

Hardware changes can be evolutionary or revolutionary: Instead of electric circuits can we use light, quantum particles, DNA…?

Computation and Automation

What can we compute and automate? Some useful sounding problems have been proven to be unsolvable. What are the limits?

A detailed discussion of these principles and the breadth of importance of computer science can be found at

For an alternate general introduction to programming and the context of C# in particular, there is another free online source, Rob Miles’ C# Yellow Book, available at Note that it is written specifically for Microsoft Windows use, using Visual Studio software development environment, which works only on Windows machines, and costs a lot if you are not a student.

The Lab: Editing, Compiling, and Running with Xamarin Studio will introduce an alternative to the Microsoft environment: Xamarin Studio and Mono, which are free, open-source software projects that make C# available for multiple platforms: Windows, Mac, or Linux machines. With a substantial fraction of students having their own machine that does not run Windows, this flexibility is important.