University of Southern California The USC Andrew and Erna Viterbi School of Engineering Pre-College Summer Programs - Student Portfolios

Truth Table

 

Switch 1 Switch 2 Switch 3 Output
0 0 0 Green
1 0 0 Yellow
0 1 0 Yellow
0 0 1 Yellow
1 1 0 Red
1 0 1 Red
0 1 1 Red
1 1 1 ALARM!!!

Boolean Algebra

- Boolean algebra is the modern digital computer logic that was developed by English mathematician George Boole in the 1840's. (Source: http://en.wikipedia.org/wiki/George_Boole)

- This type of algebra system is intended to enable humans like us to communicate with computers using different number systems to input logical statements using these numerical symbols.

- In boolean algebra, AND means X in terms of regular algebra. For example: A AND B is equal to A*B or AB.

- In boolean algebra, OR means + in terms of regular algebra. For example: A or B is equal to (A) or (B).

- In boolean algebra, inverters refer to switching a letter such as A into a letter with a bar on top such as A(bar).

- In computers, we use a hexadecimal system based on a base of 16 such as 16^5, 16^4, 16^3, 16^2, 16^1, and 16^0.

- The numbers of a hexadecimal system is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. For example, the number 16 is converted in a hexadecimal system to (1, 0) which is equal to 16^1 + 0, which is 16.

- In computers, there are 8 bits for every byte.

- There is another system used in computers as well and that is the binary number system.

- In the binary system, the only numbers used are 1 and 0. For example: 2 is equal to (1, 0) which is equal to 2^`1 + 0.

- These number systems are used to provide a logic that can be used to communicate with robots and computers that can enable them to perform various tasks.

Circuit Design with AND and OR Gates

- In circuit designs, computer logic can be used in the form of circuit gates that direct the flow of electricity from one point to another.

- In AND gates, an input of 1 and 1 is needed in order for the output to be 1 or an input of 0 and 0 for the output to be a 0. Otherwise, if a 0 is present in one of the inputs, then the output will remain a 0. In terms of an A or B input, if both inputs are A's then the output is AA but if one of the outputs is a B, then the output is AB.

- In OR gates, an input of 1 or 0 is needed in order for the output to be 1 because it is either 1 or 0 in order for the particular variable to occur in the output but if both inputs are 0 then the output is 0. Therefore, this is the complete opposite of the AND gate.

- There are also inverter gates present in the circuits that switch an input to the other input, which  is a 1 if the original input was a 0 or an A(bar) if the original input was an A. This could be placed either before or after the main AND or OR gates in the sequence of gates at the designers' discretion.

- Here is a video of Salvador designing the college admission circuit that would help us greatly with designing the actual circuit for the anti-theft device: