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Lecture 1 Class Overview and Appendix A -- Number Systems

Lecture 1 Class Overview and Appendix A -- Number Systems. Other courses in computer sequence ELEN 350 Computer Architecture and Design ELEN 449 Microprocessor Systems Design ELEN 450 Computer Interfacing and Communications ELEN 454 Digital Integrated Circuit Design

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Lecture 1 Class Overview and Appendix A -- Number Systems

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  1. Lecture 1Class Overviewand Appendix A -- Number Systems

  2. Other courses in computer sequence • ELEN 350 Computer Architecture and Design • ELEN 449 Microprocessor Systems Design • ELEN 450 Computer Interfacing and Communications • ELEN 454 Digital Integrated Circuit Design • ELEN 468 Advanced Logic Design • ELEN 472 Microelectronic Circuit Fabrication (electronics) • ELEN 473 Microelectronic Device Design (electronics) • ELEN 474 VLSI Circuit Design (electronics) • ELEN 475 Introduction to VLSI Systems Design • Careers related to Computers • VLSI • Fabrication • Programmers • System engineers • Micro-programmers (micro-processor controllers) • Others

  3. Appendix A Number Systems

  4. Positional Number Notation • Positional Number Notation • Decimal , Binary, Octal, Hexadecimal • A digit’s place in the sequence determines its weight • Decimal Numbers - Base 10 -- Digits 0-9 • Example • 15410 = =

  5. Positional Number Notation • Binary- Base 2 - Digits 0 and 1. Binary Digits (bits) • Example • 100110102 =

  6. Positional Number Notation • Octal- Base 8 - Digits 0 - 7. • Example • 2328 =

  7. Positional Number Notation • Hexadecimal- Base 16 - Digits 0 - 9, A-F • A16 = 1010 B16 = 1110 C16 = 1210 • D16 = 1310 E16 = 1410 F16 = 1510 • Example • 9A16 =

  8. Conversion Between Binary, Octal, and Hexadecimal Systems • Conversion from Binary to Octal or Hexadecimal. • Octal • Group into 3 bit groupings, starting at right. • Ex. 1 0 0 1 1 0 1 0 2 • Hexadecimal • Group into 4-bit groupings, starting at right. • Ex. 1 0 0 1 1 0 1 0 2

  9. Conversion from Octal to Hexadecimal and Hexadecimal to Octal (1) Convert to binary (2) Convert from binary to hexadecimal or octal. • Ex. 2328Convert to hexadecimal • (1) • (2) • Ex. 9A16Convert to octal • (1) • (2)

  10. Conversion from Decimal to Binary (1) Perform successive division -- successively divide the base 10 number by the base to which it is to be converted (2) Collect the remainder to form the number in the target base (3) 1st division yields the least significant bit as its remainder (4) Continue until the quotient is 0.

  11. Conversion from Decimal to Binary (1) Ex. Convert 15410 to binary

  12. Conversion from Decimal to Octal (2) Ex. Convert 15410 to octal

  13. Conversion from Decimal to Hexadecimal (3) Ex. Convert 15410 to hexadecimal

  14. Binary Arithmetic Operations • Base 10 (review) -- addition 9510 +_1610 11110 • Base 10 (review) -- subtraction 9510 -_1610 7910

  15. Binary Arithmetic Operations • Addition in Base 2 -- Laws • 0 + 0 = 0 • 0 + 1 = 1 • 1 + 0 = 1 • 1 + 1 = 0 with a carry of 1 • Ex. 1 0 12 1 0 1 1 1 1 12 1 1 1 0 0 0 0

  16. Binary Arithmetic Operations • Subtraction in Base 2 -- Laws • 0 - 0 = 0 • 0 - 1 = 1 with borrow of 1 • 1 - 0 = 1 • 1 - 1 = 0 • Ex. 1 0 0 0 02 1 0 1 1 1 1 12 1 1 0 0 0 0

  17. Homework Assignment HW #1 -- Appendix A

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