Logic gate

This is a tough week, since we need to stay in school on Saturday. Not to mention, I could not stop writing blog. I am going to mention following things in the main paragraph.

1. Data presentation poster
2. Thinking of computers
3. Boolean expressions
4. How transistors  and combined gates work
5. Boolean algebra
6. How computers add numbers

1. We made a poster 2 weeks ago. The topic is data representation, which links to previous blog. There are five parts in the poster, which are Number, Character, Image, Audio, Video. My idea here is that character, image, audio and video could be digitized into numbers using compression method. And numbers that are expressed into different base could be translated to each other. To reflection, I should say that I did not pay much attention on the terminologies and their definition because I spend too much time on the designing of the poster.

2.   Actually computers do not have their own thoughts. They just follow the instructions written by human. Those instructions are stored in the memories, and the core of computers—CPU— follow those instructions to “think”.

3. Computers are binary system, so human need to design a special computing system for them. George Boole, an English mathematician, introduced Boolean algebra, which is ideal for binary number system. Basically, the algebra are about answering questions “yes” or “no”. Logic gates are digital application of Boolean algebra, which is A device that performs a basic operation on electrical signals, accepting one or more input signals and producing a single output signal. I was taught with 6 gates, which are NOT gate, OR gate, AND gate, NAND gate, NOR gate, XOR gate. 

Not gates return opposite signals of input as output. An OR gate accepts two input signals
If both are 0, the output is 0; otherwise, the output is 1 At least one of the inputs needs to be 1. An AND gate accepts two input signals. If both are 1, the output is 1; otherwise, the output is 0. 

The NAND gate accepts two input signals. If both are 1, the output is 0; otherwise, the output is 1. The NOR gate accepts two input signals. If both are 0, the output is 1; otherwise, the output is 0. Note the difference between the XOR gate and the OR gate; they differ only in one input situation When both input signals are 1, the OR gate produces a 1 and the XOR produces a 0. XOR is called the exclusive OR because its output is 1 if either one input or the other is 1, excluding the case that they both are. 

4. A transistor acts like a switch. It has no moving parts and it’s made of a semiconductor material. A transistor has three terminals (source, base, and emitter) If the electrical signal is grounded, it is allowed to flow through an alternative route to the ground (literally) where it can do no harm. 

Gates are combined into circuits by using the output of one gate as the input for another. Three inputs require eight rows to describe all possible input combinations. This same circuit using a Boolean expression is (AB + AC). However, there are many ways of combination of the gates. For example, we did an activity that need us to create a truth table to justify the effect of the circuits. 

5. Commutative: The commutative property says that binary operations

AND and OR may be applied left to right or right to left. (A AND B is

the same as B AND A; A OR B is the same as B OR A.)

Associative: The associative property says that given three Boolean

variables, they may be ANDed or ORed right to left or left to right.

((A AND B) AND C is the same as A AND (B AND C); (A OR B) OR

C is the same as A OR (B OR C).)

Distributive: The distributive property says that given three Boolean

variables, the first AND the result of the second OR the third is the

same as the first AND the second OR the first AND the third. (A

AND (B OR C) = (A AND B) OR (A AND C). Also, the first OR the

result of second AND the third is the same as the first OR the second

AND the result of the first OR the third. (A OR (B AND C) = (A OR

B) AND (A OR C).)

Identity: The identity property says that any value A AND the OR

identity always returns A and that any value A OR the AND identity

always returns A. (A AND 1 = A; A OR 0 = A.)

Complement: The complement property says that any value AND the

compliment of that value equals the OR identity and that any value

OR the compliment of that value equals the OR identity. (A AND (A’)

= 0; A OR (A’) = 1.)

DeMorgan’s Law: DeMorgan’s Law says that the complement of A

AND B is the same as the complement of A OR the complement of B,

and the complement of A OR B is the same as the complement of B

AND the complement of A. ((A AND B)’ = A’ OR B’; (A OR B)’ = A’

AND B’).)

6. Computers use adder to add numbers. Adder are a kind of circuit that takes the carry-in value into account. For example, 

This is full adders, which is a combined circuit that uses a gate circuit to add two binary numbers and find the sum, called a full adder. A full adder can handle the low carry and output the local add carry. Multi-bit full adder can be obtained by cascading multiple one-bit adders. 

The half adder does not receive the carry input, and the full adder has a carry input. When adding two multi-bit binary numbers, except for the lowest bit, each bit must consider the carry from the lower bit. 

The characteristic of XOR is the same as adding, but do not have carry-in function. 

Conclusion, I learn lot about computers this week. Based on what I learned, I feel like computer is not magic to me any more, and it is just a machine that do what we order. Besides, I was shocked by how computer works. Logic as simple as Boolean algebra could create such machine that make human’s life a big difference!