1-1 Lecture 1 Class Overview and Appendix A -- Number Systems

1-2  Other courses in computer sequence  ELEN 350Computer Architecture and Design  ELEN 449Microprocessor Systems Design  ELEN 450Computer Interfacing and Communications  ELEN 454Digital Integrated Circuit Design  ELEN 468Advanced Logic Design  ELEN 472Microelectronic Circuit Fabrication (electronics)  ELEN 473Microelectronic Device Design (electronics)  ELEN 474VLSI Circuit Design (electronics)  ELEN 475Introduction to VLSI Systems Design  Careers related to Computers  VLSI  Fabrication  Programmers  System engineers  Micro-programmers (micro-processor controllers)  Others

1-3 Appendix A Number Systems

1-4 Positional Number Notation –Decimal, Binary, Octal, Hexadecimal –A digit’s place in the sequence determines its weight Decimal Numbers - Base Digits 0-9 –Example – = =

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

1-6 Positional Number Notation Octal- Base 8 - Digits Example =

1-7 Positional Number Notation Hexadecimal- Base 16 - Digits 0 - 9, A-F A 16 = B 16 = C 16 = D 16 = E 16 = F 16 = Example 9A 16 =

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

1-9 Conversion from Octal to Hexadecimal and Hexadecimal to Octal (1) Convert to binary (2) Convert from binary to hexadecimal or octal. Ex Convert to hexadecimal (1) (2) Ex.9A 16 Convert to octal (1) (2)

1-10 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.

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

1-12 Conversion from Decimal to Octal (2) Ex. Convert to octal

1-13 Conversion from Decimal to Hexadecimal (3) Ex. Convert to hexadecimal

1-14 Binary Arithmetic Operations Base 10 (review) -- addition _ Base 10 (review) -- subtraction _

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

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

1-17 Homework Assignment HW #1 -- Appendix A