This week, we mainly learnt Boolean Expression, logic gate and truth table.
First of all, we did our magnificent poster presentation regard to data representation. Our group’s theme was the representation of numbers and texts. However, I spent too much time explaining my part, which led to a slight imperfection of our group. I’ll notice that next time.
Boolean Expressions and Logic Gates
Before entering the main theme, Mr. Pete asked us a question: how computers think. Computers do not have their own consciousness (by now). The way that they calculate is through the logic gates, which are the best solutions for binary. The definition of Boolean expression is “Uses Boolean algebra, a mathematical notation for expressing two-valued logic”. Under this expression system, there are 8 logic gates that we learnt, and each of them has a symbol, which is also known as a logic diagram. The table that shows all possible combinations of inputs and outputs of logic gates are known as “truth table”.
NOT Gate
Output an opposite signal. All 0 to 1, and all 1 to 0. For example: You will pass the exam (1) if you you do not play too much video game (0); vice versa.
Or Gate
Fulfill at least one conditions (at least a 1 in the conditions). For example: If Bryan wins the game (1) or Kevin wins the game (1), we are having a party (1).
And Gate
Fulfill both conditions (both of them are 1). For example: If both Bryan (1) and Kevin (1) win the game, we are gonna have the a party (1).
NAND Gate
=NOT AND. Do the AND first, and then do NOT.
NOR Gate
=NOT OR. Do the OR first, and then do NOT.
XOR Gate
=Exclusive or. Fulfill either one of the conditions (one and only one of inputs is 1).
XNOR Gate
=NOT XOR. Do the XOR first, and then do NOT.
Converting Logic Statements
Sometimes, we convert a complex expression into simpler form through a truth table. For example, in a statement like this:
Mr. Fly won’t give us any assignment if group A and group B did a great job on the poster, or, if he does not show up this class.
For 8 possible combinations of inputs, there are only 5 conditions that we will not get any assignments. This help us to figure out the real situation and possibility.
Transistor and Combined Gates
Transistor is the component of logic gate. It is like switch turning on and off all the time. It is made of semiconductor, so they can work fast.
Sometimes, we combine several logic gates in a circuit to create more complex algorithm. It’s similar to converting logic statements. Base on the algorithm rules of boolean expression, we can do simplification for several gates. The following three simplifications worth knowing:
DeMorgan: (A + B)’=A’ * B’; (A * B)’=A’ + B’.
Distributive: A * (B + C)=A * B + A * C; A + B * C=(A + B) * (A + C).
Simplification: A + A’B=A + B; A * (A’ + B)=A * B
Through more complex combinations and converting, we get a way to add numbers in binary. There are three ways: XOR, Half adder and Full adder. For one digits, we can use a XOR gate, but it can only represent that digit. In order to represent carries, we expend the XOR gate into a half adder (a XOR gate and an AND gate), then a full adder (2 XOR gates, 2 AND gates and an OR gate).
HL Topic: Social Impacts of Embedded Systems
Although I was not at school, I learnt this from the class presentation and information from the Internet.
GPS: Global positioning system. 4 satellites give 4 possible regions. The overlap area is your precise location. The time difference tells the distance, which indicates the possible location.
RFID: Radio frequency identification. Provide a unique wireless identification for object. RFID tag is consisted of an antenna and a RFID. Differentiate devices connected wirelessly.
Electronic Tagging: used for prisoners. It uses GPS to locate prisoners and notice managers when prisoners are trying to take the device off. It’s a economical way to track criminals and effectively reduce crime, but ethic concerns like freedom of prisoners have to be concerned when applying.
CCTV Surveillance: Closed Circuit Television. It is used to detect whether cars are driven too fast. For mobile ones, the beam changes frequency when a car pass by to measure the speed. For fixed ones, the time difference between two points helps to measure the speed.
Upgraded Safety System: If something harmful happen that is not on the plan, a safety system will be triggered. E.g.: airbags on car.
Weekly Reflection
The things we learnt this week partially answered the question under my heart for year: how exactly the bottom layer of computers work. We learnt the basic units on a chip and how it works. It’s what every CS people should know. For HL topics, they are practical and useful. Hope I didn’t lose that class!
JIHONG ZHAO 