Number System

The technique to represent and work with numbers is called number system. Decimal number system is the most common number system. Other popular number systems include binary number system, octal number system, hexadecimal number system, etc.

Decimal Number System

Decimal number system is a base 10 number system having 10 digits from 0 to 9. This means that any numerical quantity can be represented using these 10 digits. Decimal number system is also a positional value system. This means that the value of digits will depend on its position. Let us take an example to understand this.

Say we have three numbers – 734, 971 and 207. The value of 7 in all three numbers is different−

• In 734, value of 7 is 7 hundreds or 700 or 7 × 100 or 7 × 10²
• In 971, value of 7 is 7 tens or 70 or 7 × 10 or 7 × 10¹
• In 207, value 0f 7 is 7 units or 7 or 7 × 1 or 7 × 10⁰

The weightage of each position can be represented as follows -

In digital systems, instructions are given through electric signals; variation is done by varying the voltage of the signal. Having 10 different voltages to implement decimal number system in digital equipment is difficult. So, many number systems that are easier to implement digitally have been developed. Let’s look at them in detail.

Binary Number System

The easiest way to vary instructions through electric signals is two-state system – on and off. On is represented as 1 and off as 0, though 0 is not actually no signal but signal at a lower voltage. The number system having just these two digits – 0 and 1 – is called binary number system.

Each binary digit is also called a bit. Binary number system is also positional value system, where each digit has a value expressed in powers of 2, as displayed here.

In any binary number, the rightmost digit is called least significant bit (LSB) and leftmost digit is called most significant bit (MSB).

And decimal equivalent of this number is sum of product of each digit with its positional value.

11010₂ = 1×2⁴ + 1×2³ + 0×2² + 1×2¹ + 0×2⁰

= 16 + 8 + 0 + 2 + 0

= 26₁₀

Computer memory is measured in terms of how many bits it can store. Here is a chart for memory capacity conversion.

• 1 byte (B) = 8 bits
• 1 Kilobytes (KB) = 1024 bytes
• 1 Megabyte (MB) = 1024 KB
• 1 Gigabyte (GB) = 1024 MB
• 1 Terabyte (TB) = 1024 GB
• 1 Exabyte (EB) = 1024 PB
• 1 Zettabyte = 1024 EB
• 1 Yottabyte (YB) = 1024 ZB

Octal Number System

Octal number system has eight digits – 0, 1, 2, 3, 4, 5, 6 and 7. Octal number system is also a positional value system with where each digit has its value expressed in powers of 8, as shown here −

Decimal equivalent of any octal number is sum of product of each digit with its positional value.

726₈ = 7×8² + 2×8¹ + 6×8⁰

= 448 + 16 + 6

= 470₁₀

Hexadecimal Number System

Octal number system has 16 symbols – 0 to 9 and A to F where A is equal to 10, B is equal to 11 and so on till F. Hexadecimal number system is also a positional value system with where each digit has its value expressed in powers of 16, as shown here −

Decimal equivalent of any hexadecimal number is sum of product of each digit with its positional value.

27FB₁₆ = 2×16³ + 7×16² + 15×16¹ + 10×16⁰

= 8192 + 1792 + 240 +10

= 10234₁₀

Units To Measure Size of Memory

4 Bits                   =        1 Nibble

8 Bits                   =        1 Byte

1024 Byte            =        1 Kilobyte

1024 K.Byte        =       1 Megabyte

1024 M.Byte        =        1 Gigabyte

1024 G.Byte        =       1 Terabyte

1024 T.Byte         =       1 Peta byte

1024 P.Byte         =       1 Exabyte

1024 E.Byte        =       1 Zeta byte

1024 Z.Byte         =       1 Yottabyte

Magnetic Tape

A tape is a magnetically thin coated piece of plastic wrapped around wheels capable of storing data. Tape is less expensive than other storage mediums, but it is a much slower solution because it is sequential access and is often used for backing up large amounts of data.

Today, tape has mostly been abandoned for faster and more reliable solutions like disc drives, hard drives, and flash drives that are all direct access and cloud storage. The image to the right is a picture and example of magnetic tape taken by KENPEI and shared under the creative commons.

How much can a tape drive store?

The storage capacity of a tape drive all depends on the type of tape drive and technology being used. For example, the first tape drive introduced by Remington Rand in 1951 was only capable of storing 224 KB of data. Later tape drives released in the early 2000s were capable of storing several TB of data. For example, the IBM TS1155 generation 6 tape drive released in 2017 is capable of storing 15 TB of uncompressed data.

Types of Secondary Memory

Magnetic Disk The Magnetic Disk is Flat, circular platter with metallic coating that is rotated beneath read/write heads. It is a Random Access Device; read/write head can be moved to any location on the platter 

Floppy Disk These are small removable disks that are plastic coated with magnetic recording material. Floppy disks are typically 3.5″ in size (diameter) and can hold 1.44 MB of data. This portable storage device is a rewritable media and can be reused a number of times. Floppy disks are commonly used to move files between different computers. The main disadvantage of floppy disks is that they can be damaged easily and, therefore, are not very reliable. The following figure shows an example of the floppy disk. Figure 3 shows a picture of the floppy disk. 

Hard Disk Another form of auxiliary storage is a hard disk. A hard disk consists of one or more rigid metal plates coated with a metal oxide material that allows data to be magnetically recorded on the surface of the platters. The hard disk platters spin at 5 a high rate of speed, typically 5400 to 7200 revolutions per minute (RPM).Storage capacities of hard disks for personal computers range from 10 GB to 120 GB (one billion bytes are called a gigabyte).

Optical Disks Optical Mass Storage Devices Store bit values as variations in light reflection. They have higher area density & longer data life than magnetic storage. They are also Standardized and relatively inexpensive. Their Uses: read-only storage with low performance requirements, applications with high capacity requirements & where portability in a standardized format is needed. 

Types of Optical Disk
1. CD-ROM (read only)
2. CD-R: (record) to a CD
3. CD-RW: can write and erase CD to reuse it (re-writable)
4. DVD(Digital Video Disk)

Types of Primary Memory

RAM (Random Access Memory)

The Word “RAM” stands for “random access memory” or may also refer to short-term memory. It’s called “random” because you can read store data randomly at any time and from any physical location. It is a temporal storage memory. RAM is volatile that only retains all the data as long as the computer powered. It is the fastest type of memory. RAM stores the currently processed data from the CPU and sends them to the graphics unit.

There are generally two broad subcategories of RAM:

• Static RAM: Static RAM is the form of RAM and made with flipflops and used for primary storage are volatile. It retains data in latch as long as the computer powered. SRAM is more expensive and consumes more power than DRAM. It used as Cache Memory in a computer system. As technically, SRAM uses more transistors as compared to DRAM. It is faster compared to DRAM due to the latching arrangement, and they use 6 transistors per data bit as compared to DRAM, which uses one transistor per bit.

• Dynamic Random Access Memory (DRAM): It is another form of RAM used as Main Memory, its retains information in Capacitors for a short period (a few milliseconds) even though the computer powered. The Data is Refreshed Periodically to maintain in it. The DRAM is cheaper, but it can store much more information. Moreover, it is also slower and consumes less power than SRAM.

ROM  (Read Only Memory)

ROM is the long-term internal memory. ROM is “Non-Volatile Memory” that retains data without the flow of electricity. ROM is an essential chip with permanently written data or programs. It is similar to the RAM that is accessed by the CPU. ROM comes with pre-written by the computer manufacturer to hold the instructions for booting-up the computer.

There is generally Three broad type of ROM:

• PROM (Programmable Read Only Memory): PROM stands for programmable ROM. It can be programmed only be done once and read many. Unlike ROM, PROMs retain their contents without the flow of electricity. PROM is also nonvolatile memory. The significant difference between a ROM and a PROM is that a ROM comes with pre-written by the computer manufacturer whereas PROM manufactured as blank memory. PROM can be programmed by PROM burner and by blowing internal fuses permanently.

• EPROM (Erasable Programmable Read Only Memory): EPROM is pronounced ee-prom. This memory type retains its contents until it exposed to intense ultraviolet light that clears its contents, making it possible to reprogram the memory.

• EEPROM (Electrically Erasable Programmable Read Only Memory): EEPROM can be burned (programmed) and erased by first electrical waves in a millisecond. A single byte of a data or the entire contents of device can be erased. To write or erase this memory type, you need a device called a PROM burner.

Memory

A memory is just like a human brain. It is used to store data and instructions. Computer memory is the storage space in the computer, where data is to be processed and instructions required for processing are stored. The memory is divided into large number of small parts called cells. Each location or cell has a unique address, which varies from zero to memory size minus one. For example, if the computer has 64k words, then this memory unit has 64 * 1024 = 65536 memory locations. The address of these locations varies from 0 to 65535.

Memory is primarily of three types −

• Cache Memory
• Primary Memory/Main Memory
• Secondary Memory

Cache Memory

Cache memory is a very high speed semiconductor memory which can speed up the CPU. It acts as a buffer between the CPU and the main memory. It is used to hold those parts of data and program which are most frequently used by the CPU. The parts of data and programs are transferred from the disk to cache memory by the operating system, from where the CPU can access them.

Advantages

The advantages of cache memory are as follows −

• Cache memory is faster than main memory.
• It consumes less access time as compared to main memory.
• It stores the program that can be executed within a short period of time.
• It stores data for temporary use.

Disadvantages

The disadvantages of cache memory are as follows −

• Cache memory has limited capacity.
• It is very expensive.

Primary Memory (Main Memory)

Primary memory holds only those data and instructions on which the computer is currently working. It has a limited capacity and data is lost when power is switched off. It is generally made up of semiconductor device. These memories are not as fast as registers. The data and instruction required to be processed resides in the main memory. It is divided into two subcategories RAM and ROM.

Characteristics of Main Memory

• These are semiconductor memories.
• It is known as the main memory.
• Usually volatile memory.
• Data is lost in case power is switched off.
• It is the working memory of the computer.
• Faster than secondary memories.
• A computer cannot run without the primary memory.

Secondary Memory

This type of memory is also known as external memory or non-volatile. It is slower than the main memory. These are used for storing data/information permanently. CPU directly does not access these memories, instead they are accessed via input-output routines. The contents of secondary memories are first transferred to the main memory, and then the CPU can access it. For example, disk, CD-ROM, DVD, etc.

Characteristics of Secondary Memory

• These are magnetic and optical memories.
• It is known as the backup memory.
• It is a non-volatile memory.
• Data is permanently stored even if power is switched off.
• It is used for storage of data in a computer.
• Computer may run without the secondary memory.
• Slower than primary memories.

Motherboard

A motherboard (sometimes alternatively known as the mainboard, main circuit board, system board, baseboard, planar board or logic board, or colloquially, a mobo) is the main printed circuit board (PCB) found in general purpose computers and other expandable systems. It holds and allows communication between many of the crucial electronic components of a system, such as the central processing unit (CPU) and memory, and provides connectors for other peripherals. Unlike a backplane, a motherboard usually contains significant sub-systems such as the central processor, the chipset's input/output and memory controllers, interface connectors, and other components integrated for general purpose use and applications.

Motherboard specifically refers to a PCB with expansion capability and as the name suggests, this board is often referred to as the "mother" of all components attached to it, which often include peripherals, interface cards, and daughtercards: sound cards, video cards, network cards, hard drives, or other forms of persistent storage; TV tuner cards, cards providing extra USB or FireWire slots and a variety of other custom components.

Similarly, the term mainboard is applied to devices with a single board and no additional expansions or capability, such as controlling boards in laser printers, televisions, washing machines, mobile phones and other embedded systems with limited expansion abilities.

CPU

The central processing unit (CPU) is the unit which performs most of the processing inside a computer. To control instructions and data flow to and from other parts of the computer, the CPU relies heavily on a chipset, which is a group of microchips located on the motherboard.

The CPU has two components:

• Control Unit: extracts instructions from memory and decodes and executes them
• Arithmetic Logic Unit (ALU): handles arithmetic and logical operations

To function properly, the CPU relies on the system clock, memory, secondary storage, and data and address buses.

This term is also known as a central processor, microprocessor or chip

Techopedia explains Central Processing Unit (CPU)

The CPU is the heart and brain of a computer. It receives data input, executes instructions, and processes information. It communicates with input/output (I/O) devices, which send and receive data to and from the CPU. Additionally, the CPU has an internal bus for communication with the internal cache memory, called the backside bus. The main bus for data transfer to and from the CPU, memory, chipset, and AGP socket is called the front-side bus.

The CPU contains internal memory units, which are called registers. These registers contain data, instructions, counters and addresses used in the ALU's information processing.

Some computers utilize two or more processors. These consist of separate physical CPUs located side by side on the same board or on separate boards. Each CPU has an independent interface, separate cache, and individual paths to the system front-side bus. Multiple processors are ideal for intensive parallel tasks requiring multitasking. Multicore CPUs are also common, in which a single chip contains multiple CPUs.

CPU Overview

The picture below is an example of what the top and bottom of an Intel Pentium processor may look. The processor is placed and secured into a compatible CPU socket found on the motherboard. Processors produce heat, so they are covered with a heat sink to keep them cool and running smoothly.

As you can see in the above picture, the CPU chip is usually in the shape of a square or rectangle and has one notched corner to help place the chip properly into the CPU socket. On the bottom of the chip are hundreds of connector pins that plug into each of the corresponding holes in the socket. Today, most CPU's resemble the picture shown above. However, Intel and AMD have also experimented with slot processors that were much larger and slid into a slot on the motherboard. Also, over the years, there have been dozens of different types of sockets on motherboards. Each socket only supports specific types of processors and each has its own pin layout.

What does the CPU do?

The CPU's main function is to take input from a peripheral (keyboard, mouse, printer, etc) or computer program, and interpret what it needs. The CPU then either outputs information to your monitor or performs the peripheral's requested task.

The CPU was first developed at Intel with the help of Ted Hoff and others in the early 1970s. The first processor released by Intel was the 4004 processor, shown in the picture to the right.

Components of the CPU

In the CPU, there are two primary components.

1.    ALU (arithmetic logic unit) - performs mathematical, logical, and decision operations.

2.    CU (control unit) - directs all the processors operations.

Over the history of computer processors, the speed (clock speed) and capabilities of the processor have dramatically improved. For example, the first microprocessor was the Intel 4004 that was released on November 15, 1971, and had 2,300 transistors and performed 60,000 operations per second. The Intel Pentium processor has 3,300,000 transistors and performs around 188,000,000 instructions per second.

Types of CPUs

In the past, computer processors used numbers to identify the processor and help identify faster processors. For example, the Intel 80486 (486) processor is faster than the 80386 (386) processor. After the introduction of the Intel Pentium processor (which would technically be the 80586), all computer processors started using names like Athlon, Duron, Pentium, and Celeron.

Today, in addition to the different names of computer processors, there are different architectures (32-bit and 64-bit), speeds, and capabilities. Below is a list of the more common types of CPUs for home or business computers.

Note:

There are multiple versions for some of these CPU types.

AMD processors

K6-2 K6-III Athlon Duron Athlon XP

Sempron Athlon 64 Mobile Athlon 64 Athlon XP-M Athlon 64 FX

Turion 64 Athlon 64 X2 Turion 64 X2 Phenom FX Phenom X4

Phenom X3 Athlon 6-series Athlon 4-series Athlon X2 Phenom II

Athlon II E2 series A4 series A6 series A8 series A10 series

Intel processors

4004 8080 8086 8087 8088 80286 (286) 80386 (386) 80486 (486)

Pentium Pentium w/ MMX Pentium Pro Pentium II Celeron Pentium III Pentium M Celeron M

Pentium 4 Mobile Pentium 4-M Pentium D

Pentium Extreme Edition Core Duo Core 2 Duo

Core i3 Core i5 Core i7

 How fast does a CPU transfer data?

As with any device that utilizes electrical signals, the data travels very near the speed of light, which is 299,792,458 m/s. How close to the speed of light a signal can get depends on the medium (type of metal in the wire) through which the signal is traveling. Most electrical signals are traveling at about 75 to 90% the speed of light.

Could a GPU be used in place of a CPU?

No. Although GPU's can process data and do many of the same things as a CPU, it lacks the ability to perform many of the functions required by typical operating systems and software.

Could a computer work without a CPU?

No. All computers require some type of CPU.

Types of Digital Computer

On the basis of size and processing speed, there are four types of digital computer

1.    ​Super Computer

2.    ​Mainframe Computer

3.    ​Mini Computer

4.    Micro Computer

Super Computer

The most powerful computers in terms of performance and data processing are the Supercomputers. These are specialized and task specific computers used by large organizations. These computers are used for research and exploration purposes, like NASA uses supercomputers for launching space shuttles, controlling them and for space exploration purpose.

The supercomputers are very expensive and very large in size. It can be accommodated in large air-conditioned rooms; some super computers can span an entire building.

Seymour Cray designed the first Supercomputer “CDC 6600” in 1964. CDC 6600 is known as the first ever Supercomputer. The name of first Indian super computer is Parma 10000. This super computer is developed by C-DAC (Center for Development of Advance Computing) some other Indian super computers are Anurag, Param Padma etc.

Exascale Super Computer

On 29th July, 2015, President of the United States, Barack Obama, approved the development of an Exascale Super Computer. The Exascale Super computer will be 30 times faster and more powerful than today’s fastest Super Computers. The need to develop such a high performance Supercomputer comes after China’s surge in high performance computing. However, the US still tops the list of Supercomputers with 233 high performance machines. China has 37 Supercomputers but they lead the list of the most powerful and high performance supercomputers since June 2013.

Presently, China’s “Tianhe – 2” is the world’s faster Supercomputer.

The Tianhe – 2 can perform 100 Petaflops, i.e quadrillions of floating point operations per second.

In Pakistan Supercomputers are used by Educational Institutes like NUST for research purposes. Pakistan Atomic Energy commission & Heavy Industry Taxila uses supercomputers for Research purposes.
Space Exploration

Supercomputers are used to study the origin of the universe, the dark-matters. For these studies scientist use IBM’s powerful supercomputer “Roadrunner” at National Laboratory Los Alamos.​
Earthquake Studies

​Supercomputers are used to study the Earthquakes phenomenon. Besides that, supercomputers are used for natural resources exploration, like natural gas, petroleum, coal, etc.
​Weather Forecasting

​Supercomputers are used for weather forecasting, and to study the nature and extent of Hurricanes, Rainfalls, windstorms, etc.
​Nuclear Weapons Testing

​Supercomputers are used to run weapon simulation that can test the Range, accuracy & impact of Nuclear weapons.
​Popular Super Computers

• IBM’s Sequoia, in United States
• Fujitsu's K Computer in Japan
• IBM's Mira in United States
• IBM's SuperMUC in Germany
• NUDY Tianhe-1A in china

Mainframe Computer

Although Mainframes are not as powerful as supercomputers, but certainly they are quite expensive nonetheless, and many large firms & government organizations uses Mainframes to run their business operations. The Mainframe computers can be accommodated in large air-conditioned rooms because of its size. Super-computers are the fastest computers with large data storage capacity, Mainframes can also process & store large amount of data. Banks educational institutions & insurance companies use mainframe computers to store data about their customers, students & insurance policy holders.

Popular Mainframe Computers

• Fujitsu's ICL VME
• Hitachi's Z800

Mini Computer

Minicomputers are used by small businesses & firms. Minicomputers are also called as “Midrange Computers”. These are small machines and can be accommodated on a disk with not as processing and data storage capabilities as super-computers & Mainframes. These computers are not designed for a single user. Individual departments of a large company or organizations use Mini-computers for specific purposes. For example, a production department can use Mini-computers for monitoring certain production process.

Popular Mini Computers

• K-202
• Tesax Instrument TI-990
• SDS-92
• IBM Midrange Computers

Micro Computer

Desktop computers, laptops, personal digital assistant (PDA), tablets & smartphones are all types of microcomputers. The micro-computers are widely used & the fastest growing computers. These computers are the cheapest among the other three types of computers. The Micro-computers are specially designed for general usage like entertainment, education and work purposes. Well known manufacturers of Micro-computer are Dell, Apple, Samsung, Sony & Toshiba.

Desktop computers, Gaming consoles, Sound & Navigation system of a car, Netbooks, Notebooks, PDA’s, Tablet PC’s, Smartphones, Calculators are all type of Microcomputers.