Computer Programming Notes - Week 1
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- Melina Pitts
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1 Computer Programming Notes - Week 1 January 8, Logical Gates There are several basic logical gates that we will use. Each of them (except the NOT gate) take two boolean inputs and produce one boolean output. A boolean input/output is either True or False. A NOT gate takes only one input and returns an output. 1.1 AND Gate An AND gate is drawn: A B ( A AND B ) T T T Its truth table is: T F F F T F F F F It behaves just like the conjunction in English. Both inputs must be true in order for it to result in true. Just like saying Maclay is a school and it is in Tallahassee is true but Maclay is a school and it is in Europe is false. 1.2 OR Gate An OR gate is drawn: A B ( A OR B ) T T T Its truth table is: T F T F T T F F F It behaves just like the conjunction in English. One or both of the inputs must be true in order for the statement to be true. For example, Maclay is a school or it is a restaurant is true as well as Maclay is a school or it is in Tallahassee. 1
2 1.3 NOT Gate A NOT gate is drawn: A NOT A Its truth table is: T F This gate only takes in one input and just F T reverses it. So True goes to False and False goes to True. 1.4 XOR Gate An XOR gate is drawn: A B ( A XOR B ) T T F Its truth table is: T F T F T T F F F XOR stands for Exclusive OR. It is an OR gate, but it does not return True if all the inputs are True. So Maclay is a school XOR it is in Tallahassee is false while Maclay is a school XOR it is in Europe is True. 1.5 NAND Gate A NAND gate is drawn: A B ( A NAND B ) T T F Its truth table is: T F T F T T F F T A NAND gate is just the negation of an AND gate. You can think of it as an AND gate with its output being run through a NOT gate. A NAND gate is what is known as a universal gate, meaning any logical gate can be simulated using a NAND gate. For example, an AND gate can be built from NANDs like this: 2
3 1.6 OR Gate A NOR gate is drawn: A B ( A NOR B ) T T F Its truth table is: T F F F T F F F T Similarly to NAND, a NOR gate is just a negation of the OR gate. 2 Inputs Using boolean logic gates, each wire can take on two values, True or False. So, if we have n wires, there are 2 n possible inputs. This is because each wire s value is independent of every other wire s value. So, if I have two wires, and I choose a value for one of them, the other wire can still be set to both the possible values. Therefore, there are 2 2 = 4 possible input configurations. If instead of each wire being able to take on two values, it can take on three values, and I have n wires, we now can have 3 n possible input configurations. In general, if we have a possible states for each wire and n wires, there are a n input configurations. 3 Breadboards and Electronics 3.1 Breadboard A breadboard is a tool for constructing electronic circuits. There are several parts of a breadboard: a power strip, ground strip, the prototyping area, and the ravine. 3
4 On the above right board, the vertical red strips are power, the vertical blue strips are ground, and the horizontal red strips are the prototyping area. The vertical line that separates the horizontal strips is the ravine. 3.2 LED An LED, or Light Emitting Diode, is an electronic component that can emit light when a current is flowing through it. 4
5 An LED has two legs, one of which will be longer than the other. The longer leg is the positive side and the shorter one is negative. Current must flow into the positive side and out of the negative side. An LED will not work if this is reversed. 3.3 Integrated Circuits An integrated circuit is a device that can be used to implement logical circuits on a breadboard. Usually, an integrated circuit has several copies of a logical gate inside of it. For example, the following integrated circuit has 4 OR gates inside of it. 5
6 The PIN labeled VDD (14) is the power pin, while VSS (7), sometimes written GND, is the grounding pin. An integrated circuit is generally situated over the ravine so that currents flowing into a pin on one side will not affect the pin directly across from it. 6
7 7
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