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Computer Architecture and Number Systems

Understand the core components of a computer, from memory units to input/output devices, and learn about data representation and number systems. Dive into binary, decimal, and hexadecimal systems, and explore how information is stored and accessed in computing.

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Computer Architecture and Number Systems

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  1. Computer Architecture and Number Systems Topics • What is Computer? • Major Computer Components • Computer Components Interconnection • Data Representation • Bits, Bytes, and Words • The Decimal Number System • The Binary Number System • Converting from Binary to Decimal, Decimal to Binary • The Hexadecimal Number System • Converting from Hexadecimal to Decimal, Decimal to Hexadecimal

  2. What is Computer? • A data processing machine capable of performing computations and making logical decisions very fast. • Consists of hardware such as keyboard, screen, mouse, disks, memory, CD-ROM, and processing units. • A program (software) is a set of instructions written in a computer language that runs on a computer.

  3. Major Computer Components • Memory Unit (Main Memory, Secondary Storage Unit) • Arithmetic and Logic Unit (ALU), Central Processing Unit (CPU) • Input/Output (I/O) Unit

  4. Memory Unit • Memory unit stores information such as computer programs, data, or documents. • Two types of memory devices: • Primary Storage or Main Memory • Secondary Storage

  5. Memory Unit (con’t) • Main memory is fast and expensive . • Stores frequently accessed information such as programs and data during their execution. • Is volatilestorage. That is, if power is lost, the information in main memory is lost. • Secondary storage is slower and cheaper. • Disks (floppy, hard, removable), Tapes, CDs, DVDs. • Is non-volatile, that is persistent (permanent) storage.

  6. Memory Unit (con’t) • Main memory consists of a collections of storage locations. • Data are read from or written to memory in cells. A cellcan be 8 – 64 bits. • Address is used to uniquely identify a cell location. • Cells may be grouped into words. E.g., four 8-bit cells forms one word.

  7. Memory Unit (con’t) • Memory Access Methods • Sequentialaccess memory • Read memory address one after another, e.g. tape. • Random-access memory (RAM) • Any location can be read by specifying its address, e.g. main memory, disks, CDs, DVDs.

  8. Input/Output (I/O) Unit • Input/Output Unit • Input unit accepts input data and programs from an input device. • Output unit sends the results of processing (output) to an output device. • More generally, these devices are known as peripheral devices. • Input device - keyboard, mouse, scanner • Output device - monitor, printer • I/O device - disk drive (floppy, hard, removable), CD or DVD drive

  9. ALU, CPU • ALU performs calculations(such as addition, subtraction, multiplication, division) and logicaloperations (e.g. comparing two numbers). • CPU is the “brain” of the computer. • Controls operations of other components, memory, ALU, I/O. • Tells input unit when info is ready to be read into the memory unit. • Tells output unit when to send info from the memory unit to an output device.

  10. Computer Components Interconnection • CPU and memory are connected by a bus. • Connecting I/O devices • I/O devices are slower than CPU/memory. • Can’t connect directly to Bus. Need an I/O controlleror interface to handle the differences in speed between the I/O device and the bus. • A bus is a group of parallel wires that carry control signals and data between CPU and memory.

  11. Computer Components Interconnection • Three types of Bus - • Data Bus • Address Bus • Control Bus • Data bus consists of many wires. Each wire carries 1 bit at a time. The # of wires (bits) needed = size of a word. If the word is 32 bits in a computer, then we need 32-bit data bus.

  12. Computer Components Interconnection • Address bus allows access to a particular word in a memory. The number of wires = log2(total number of memory words). If the memory has 2n words, address bus needs to carry n bits at a time. • Control bus carries communication signals between CPU and memory. The number of bits used = log2(total number of control commands).

  13. Data Representation Data types: • Text • Number • Image • Audio • Video

  14. Bits, Bytes, and Words • A bit is a single binary digit (a 1 or 0). • A byte is 8 bits • A word is 32 bits (that is, 4 bytes) • Long word = 8 bytes = 64 bits • Quad word = 16 bytes = 128 bits • Programming languages use these standard number of bits when organizing data storage and access. • What do you call 4 bits? (hint: it is a small byte)

  15. Number Systems • The data in memory is represented in terms of 1’s and 0’s. • Therefore, thinking about how information is stored in RAM requires knowledge of the binary(base 2) number system. • Let’s review the decimal(base 10) number system first.

  16. The Decimal Number System • The decimal number system is a positional number system. • Example: • 1 2 6 5 5 X 100 = 5 • 103 102 101 100 6 X 101 = 60 • 2 X 102 = 200 • 1 X 103 = 1000

  17. The Decimal Number System (con’t) • The decimal number system is also known as base 10. The values of the positions are calculated by taking 10 raised to some power. • Why is the base 10 for decimal numbers? • Because we use 10 digits, the digits 0 through 9.

  18. The Binary Number System • The binary number system is also known as base 2. The values of the positions are calculated by taking 2 to some power. • Why is the base 2 for binary numbers? • Because we use 2 digits, the digits 0 and 1.

  19. The Binary Number System (con’t) • The binary number system is also a positional numbering system. • Instead of using ten digits, 0 - 9, the binary system uses only two digits, 0 and 1. • Example of a binary number and the values of the positions: • 1001101 • 26 25 24 23 22 21 20

  20. Converting from Binary to Decimal • 1001001 1 X 20 = 1 • 26 25 24 23 22 21 20 0 X 21 = 0 • 0 X 22 = 0 • 20 = 1 24 = 16 1 X 23 = 8 • 21 = 225 = 320 X 24 = 0 • 22 = 426 = 640 X 25 = 0 • 23 = 81 X 26 = 64 7310

  21. Converting from Binary to Decimal (con’t) Practice conversions: BinaryDecimal 101 1101 101101

  22. Converting From Decimal to Binary (con’t) • Perform successive divisions by 2, placing the remainder (0 or 1) in each of the positions from right to left. • Continue until the quotient is zero. • Example: 4410 • 44 / 2 = 22 rem = 0 • 22 / 2 = 11 rem = 0 • 11 / 2 = 5 rem = 1 • 5 / 2 = 2 rem = 1 • 2 / 2 = 1 rem = 0 • 1 / 2 = 0 rem = 1 • Done answer = 1 0 1 1 0 0 2

  23. Converting From Decimal to Binary (con’t) Practice conversions: DecimalBinary 59 82 175

  24. Working with Large Numbers • 1 1 0 1 0 0 0 0 1 0 1 0 0 1 1 0 = ? • Humans don’t work well with binary numbers; there are too many digits to deal with. • Memory addresses and other data can be quite large. Therefore, we sometimes use the hexadecimal number system.

  25. The Hexadecimal Number System • The hexadecimal (hex) number system is also known as base 16. The values of the positions are calculated by taking 16 to some power. • Why is the base 16 for hexadecimal numbers ? • Because we use 16 symbols, the digits 0 and 1 and the letters A through F.

  26. The Hexadecimal Number System (con’t) • Example of a hexadecimal number and the values of the positions: • 3C8B051 • 166 165 164 163 162 161 160

  27. The Hexadecimal Number System (con’t) BinaryDecimalHexadecimalBinaryDecimalHexadecimal 0 0 0 1010 10 A 1 1 1 1011 11 B 10 2 2 1100 12 C 11 3 3 1101 13 D 100 4 4 1110 14 E 101 5 5 1111 15 F 110 6 6 111 7 7 1000 8 8 1001 9 9

  28. Converting From Hexadecimal to Decimal • Example: Convert 1A5F16 to decimal. • 1A5F • 163 162 161 160 • 4096 256 16 1 • Recall: A16 = 1010 and F16 = 1510. • = 1 x 4096 + A x 256 + 5 x 16 + F x 1 • = 1 x 4096 + 10 x 256 + 5 x 16 + 15 x 1 • = 4096 + 2560 + 80 + 15 • = 675110

  29. Converting From Decimal to Hexadeciaml • Perform successive divisions by 16, placing the remainder (0-9, A-F) in each of the positions from right to left. • Continue until the quotient is zero. • Example: Convert 14310 to hex. • 143 / 16 = 8 rem = 1510 = F16 • 8 / 16 = 0 rem = 8 • Done answer = 8F16 • To Check: 8 x 16 + 15 = 128 + 15 = 14310

  30. Example of Equivalent Numbers • Binary: 1 0 1 0 0 0 0 1 0 1 0 0 1 1 12 • Decimal: 2064710 • Hexadecimal: 50A716 • Notice that the number of digits needed is smaller as the base increases.

  31. Next Class • Operating System and Using Linux. • Homework #1 due beginning of class on September 9.

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