Section 1.2 Computational Devices
Computers and computational devices are electronic machines designed to process and manipulate data, perform calculations, and execute instructions to solve problems or perform specific tasks. They are the foundation of modern technology and play a crucial role in various aspects of our lives, from personal communications to complex weather predictions.
Computational devices come in many shapes and sizes. They range from small microprocessors found in your smart thermostat to very large multiprocessor systems that execute computations at ever-increasing speeds.
All computational devices have similar characteristics and are made up of the same or similar key components.
- Hardware: Computers consist of physical components that perform the actual computations. The hardware includes the central processing unit (CPU), which serves as the "brain" of the computer and executes instructions. Other important hardware components include memory (RAM), storage devices (hard drives, solid-state drives), input devices (keyboard, mouse), output devices (monitor, printer), and various peripheral devices (USB devices, network cards, etc.).
- Software: Software refers to the programs and instructions that tell the hardware what to do. It includes operating systems (such as Windows, macOS, or Linux) that manage the computer’s resources, as well as application software that performs specific tasks or provides services. Software is typically written in programming languages and compiled or interpreted into machine code that the hardware can understand and execute.
- Data Representation: Computers use binary representation, which means they store and manipulate data in the form of binary digits (bits). Binary digits are either 0 or 1, and they can represent various types of information, such as numbers, text, images, and sound. Higher-level abstractions are used to interpret and manipulate data, allowing for complex operations and computations.
- Processing and Execution: Computers perform computations by executing instructions sequentially. These instructions are represented in machine code, which is a low-level language that the CPU can directly understand and execute. The CPU fetches instructions from memory, decodes them, and performs the necessary calculations or operations. The results are then stored back in memory or sent to output devices.
- Input and Output: Computers interact with users and the external world through input and output devices. Input devices, like keyboards and mice, allow users to provide data and instructions to the computer. Output devices, such as monitors and printers, display or present the results of computations or provide information to users. Other input and output devices include scanners, microphones, speakers, and various sensors used in embedded systems.
- Connectivity and Networking: Computers can be connected to networks, allowing them to communicate and share data with other devices. This enables tasks like accessing the internet, transferring files, sharing resources, and remote collaboration. Networking protocols and technologies, such as Ethernet and Wi-Fi, facilitate data exchange between computers and other devices.
It is worth taking a moment to understand what is meant by binary data representation. If you could look at computer memory and see the data stored, you’d see that all memory locations can store only two states. Depending upon the kind of memory, these two state are represented in different ways: charged or neutral, a local magnetic field pointing up or down, reflective or dispersive of a laser, conductive or not. We represent these two states as 0 and 1, and call them bits. Also, we always consider bits in groups of 8, called bytes. One byte is composed of eight ordered bits.
We can translate a byte into a base-10 number by defining each bit as contributing a value equal to a power of 2 to a final sum. To compute a base-10 number from a byte, we find all its bits with a value of 1 and add up the corresponding powers of 2. For example, the rightmost bit in a byte is assigned to the value \(2^0 = 1\text{.}\) If the rightmost bit in a byte is 1 (i.e.
00000001), than we add \(2^0 = 1\) to a total sum, and so the byte 00000001 encodes the base-10 number 1. If the bit is 0, we skip it when forming the final base-10 value. If both the first and second bits from the right in a byte are set to 1 (i.e. 00000011) then the encoded base-10 value of the byte 00000011 is \(2^1 + 2^0 = 2 + 1 = 3\text{,}\) and so on.Use the interactive widget below to check your understanding. The widget illustrates the bits from two sequential bytes, where the byte on the left encodes even larger powers of 2. Click each bit to toggle its value and watch how the encoded base-10 number changes. Make sure you understand how the bits of a byte form a base-10 number.
Here are a few challenges and additional things to consider.
- What is the binary representation for the decimal number 255?
- Can you encode all the base-10 numbers 0, 1, through 10 in binary?
- Do you see a pattern in the way bits are flipped as you count up?
- What is the maximum base-10 number that can be represented by the bits of one byte?
- How might we represent negative numbers?
Computers and computational devices have revolutionized the way we work, communicate, learn, and entertain ourselves. They have become an integral part of industries such as finance, healthcare, transportation, and entertainment, driving innovation and transforming society as a whole. Understanding what they can, and what they cannot do, is critical to being a knowledgeable and productive participant in society. Furthermore, understanding how programming languages work is our way in to the world of computational devices.
