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Computer Architecture and Number Systems

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

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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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