3. Application of binary number, logic and logic gate

In the previous example we talked about a lot of devices, such as flashlights, relays, and two encodings: Morse code and Braille Braille, which are very much connected to our well-known binary numbers.

Binary numbers we already know, and here are a few examples:

1. Determine the quality of the film. We pulled the film apart and found 12 squares, made of silver and black. Silver is a conductor, can conduct electricity, and black, is coated with a layer of insulating body. These 12 numbers are followed by DX encoding. Exposure speed is based on a class that has not been established by the Standard Association ASA, the first of the 12 squares is usually silver, or 1, and we can determine the exposure speed of the film by encoding 2, 3, 4, 5, 6 to describe the class given by the ASA. and 8, 9, 10 is used to encode the film, 11, 12 points out the exposure format, that is, black and white flushing.

2. UPC is a barcode that we buy in our daily life, and we don't seem to have anything to do with binary code, in fact, it's encoded by a binary code. We see that UPC is made up of bars with staggered widths and widths, and there are numbers below. UPC is made up of 30 vertical black stripes of different widths. The way we decode it is that there are black stripes where 1, White is 0. The narrowest black stripe represents a 1, and the second narrow black stripe represents 2 1. Similarly, the narrowest white gap is 1 0, and the second narrow White gap is 2 0. So we have a 95-bit binary number, and the first three bits 101 is a left guard line, indicating that the bar code starts. The rightmost three-bit is the right guard line, usually 101, the left guard line is followed by a 6-bit string, a group of 7 bits, the middle of a 5-bit middle guard line, usually 01010, indicating that the left side has ended, start to the right, the right is also 6 sets of bit strings, a group of 7 bits. The number on the left begins with 0, ends with 1, and the number on the right is the opposite. So we can translate 12 decimal numbers according to the left and right numbers, which are 12 pairs of bits, which is the 12 numbers below the bar code. The last one is used for validation. UPC supports two-direction read.

Understanding the application of binary, we put forward the logic, logic is proposed by Socrates, the most famous is the three-paragraph theory. Next is the Boolean algebra proposed by the Boolean, his breakthrough is that compared to the traditional algebra, he is the operand of the abstract, so that the operand represents a class, Boolean algebra includes: And, or, not, 1, 0. We can actually convert any Boolean expression into a circuit made up of switches and lights, The result of the light-out judgment expression. But the incandescent lamp was still not invented before Boer died. Next introduce a computer revolution of the Idol-level people: Babbage. He invented the difference machine and the analysis engine, which is the predecessor of the computer.

We talked about logic, and then we talked about the logical gate, the logic gate is actually the same as the general gate, but here is allowed to stop the current through, before the Boolean expression can be converted to a lot of locking composed of complex circuit, but this conversion after a long time, and finally by the MIT Shannon issued the " Symbolic analysis of relays and switching circuits This paper proposes that this circuit is called a network. The relay that we talked about is the device that amplifies the signal can replace the switch, the advantage is that the switch is a person to drive, but the relay can be driven by other relays, relays are also called buffers, because we can buffer for a period of time, we use "trigger" to indicate relay power, relay is also known as double throw relay, Because the output can be in two ways, and the two ways work the opposite way.

There are 4 types of logic gates:

(1) With the door: the input end of the gate can be greater than 2. A relay is used for an input terminal.

(2) or door: the input end of the gate can be greater than 2. One input terminal with a relay.

(3) and non-gate.

(4) or non-gate.

Another output of a double throw relay is called a reverse device. There is only one output, the input is 0, and the output is 1.

2-4 Decoder: 2 input, 4 output, the output is mutually exclusive, not at the same time 1.