CSC 107 – Programming For Science

George Boole  Mathematician from English middle-class  Lived from 1815 – 1864  Started work at age 16 as a teaching assistant  Held two assistantships to support family  Opened own school after many years of work  Reached pinnacle of any job -- named a Professor  Wrote Mathematical Analysis of Logic in 1847

Mathematical Analysis of Logic  Boole’s book proposed new logical system  World began with 2 values– though more created  Devised rules to add, subtract, & multiply  Work ignored during Boole’s lifetime  System only had 2 values, so what was the point?  Basis for most technology in the modern age  All it took was a simple little discovery…

Gate  Combines input(s) to generate output signal  Like most electronics, uses “on-off” state  Input is "off", if line drops below 2 volts  From volts, an input is considered on  Gate is deep fried silicon if line goes above 5 volts,  Like Boole’s logic, electronics have 2 values  Simple gates combine to make modern circuitry  All initially part of Boolean algebra  Basis of programming at the lowest, rawest level

Truth Table  Normal way that Boolean functions presented  All combinations of inputs shown in this table  This is really easy, inputs must be true or false  Output shown for each of the possible inputs  Given how it sounds, not at all complicated  Very simple rules to follow to construct  Does requires you count up to 2

NOT Gate  Simplest gate: computes opposite of input  Output false when input true;  Output true when input false;  Written in C++ as !a  a is gate’s input  x is gate’s output ax!a!a true false a x

OR Gate  Equivalent to addition in Boolean algebra  If either input is true is going to be checked  True when either a OR b are true; false otherwise  Written in C++ as a || b  a & b are inputs; x is output abx a || b false true false true a b x

AND Gate  Equivalent to multiplication in Boolean algebra  If both inputs are true is going to be checked  True when a AND b are true; false otherwise  Written in C++ as a && b  a & b are inputs; x is output abxa && b false true false true a b x

Gates in Computers  Computers more comfortable using numbers  Plus, far less to write down in truth tables  Use 0 to stand for false; Use 1 rather than true  For example of this, consider power symbol  Just a combination of 0 & 1  Ultimately, gate’s meaning does not change  Use what is easier: C++ switches back and forth

Your Turn  Get in groups of 3 & work on following activity

For Next Lecture  Read sections 7.2 – for Monday  How can we differ what our program does?  How are bool variables and operations used?  Why are if - else statements so important  Week #3 weekly assignment due Tuesday  Problems available on Angel  If problem takes more than 10 minutes, TALK TO ME!