Compiled by : Mr. Mark Anthony P. Cezar ( Lecture )

Numbers(s) A number is a mathematical object used to count and measure. Classification of numbers Natural Numbers Integers Rational Numbers Complex Numbers Computable Numbers Chapter II Introduction to Numeric and Binary System

Binary Numeral System or Binary Number System  Base-2 number system  Numeric values using two symbols 0 and 1  Used internally by almost all modern computers  Is a writing system of expressing numbers with symbol  The words binary comes from “Bi” MEANING TWO” Example: Bicycle, Binocular Example: The number 10 means 2 in decimal Why?

"There are 10 kinds of people in the world, those who understand binary numbers, and those who don't."

The BIT as a starting point....

Bit is the smallest unit of data. Where as, Binary Number is made up of only 0s and 1s

Number System Conversion

As computer programmer, it is important to know the different numeral system.

Same as...

BINARY ADDITION

BINARY SUBTRACTION

QUIZ

AdditionSubtraction

BINARY MULTIPLICATON

BINARY DIVISION

Binary Multiplication 1.10 x 10 = x 11 = x 10= x 11 = x 101 = Binary Division / 10 = /11 = /100 = /11 = / 10 =

Answer Multiplication 1-5 Answer Division 1-5

Do not just think...Analyze. Know the logic.. ….. You have a fox, a chicken and a sack of grain. You must cross a river with only one of them at a time. If you leave the fox with the chicken he will eat it; if you leave the chicken with the grain he will eat it. How can you get all three across safely? MIND TEASER

Chapter II Logic Circuits Variables, functions, truth tables, gates and networks

Digital Logic  Logic Circuit used to build computer  Logic circuit perform operation on digital signals  The general form of logic circuit is a switching network  In binary Logic circuits are only two values 0 and 1  Digital Hardware  Late 1960s and early 1970s saw a revolutionary in digital capability – smaller transistors -larger chip size  More transistor/chip gives greater functionality  Integrated circuits are fabricated on silicon wafers  Chips have tens to million transistor  Provides motivation for computer based design techniques

15 Minutes Review

quiz 1.z=tb+c 2.wxyx wy not(x) + wy

Quiz

Chapter III Logic Circuits Synthesis using AND, OR, and NOT gates Optimized Implementation of Logic Functions: Karnaugh Maps and Minimum Sum-of-Product Forms

Example logic circuit design Assume we want to design a logic circuit with three inputs x, y, and z The circuit output should be 1 only when x=1 and either y or z (or both) is 1 – Three possible combinations x=1, y=0, z=1 => xy’z x=1, y=1, z=0 => xyz’ x=1, y=1, z=1 => xyz The function could be written as – f(x,y,z)=xy’z+xyz’+xyz

Example logic circuit design

The Karnaugh map (K-map) provides a systematic (and graphical) way of performing this operation Minterms can be combined by 14a when they differ in only one variable – f(x,y,z) = xyz+xyz’ = xy(z+z’) = xy(1) = xy The K-map illustrates this combination graphically Karnaugh map

Programmable logic devices, what are they? Integrated circuit that you program using a hardware description language such as VHDL or Verilog. -Languages that you may have heard of are CUPL or ADA. With the correct tools you can even generate a schematic that is used to build the file that will be used to program the device