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# Code 11 논리 게이트

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### Code 11 논리 게이트

1. 1. Code Ch.11 빌 게이츠? 논리 게이트! chois7913년 2월 3일 일요일
2. 2. Each switch in this circuit is labeled with a letter—the same letters as in — Boolean expression. (W means NOT W and is an alternative way to w 1 − W). Indeed, if you go through the wiring diagram from left to right s ing at the top and moving from top to bottom, you’ll encounter the le About This Chapter in the same order that they appear in the expression. Each × sign in expression corresponds to a point in the circuit where two switches groups of switches) are connected in series. Each + sign in the expres corresponds to a place in the circuit where two switches (or group • Chapter 10 switches) are connected in parallel. As you’ll recall, the salesperson first brought out an unneutered tan m • “하얀색이나 황갈색의 중성화된 수컷 고양이나, Close the appropriate switches: 검정 고양이를 원해요” 하얀색이 아닌 중성화된 암컷 고양이, 또는 • 색상: 하얀색(W), 황갈색(T), 검정(B) W M N • 중성화: N T • 수컷(M) / 암컷(F) F N W • 이를 위한 논리식 B • (M x N x (W + T)) + (F x N x (1 - W)) + B • 이 장에서는 • 논리식을 이용해서 회로를 간단하게 만들기 Although the M, T, and NOT W switches are closed, we don’t have a c plete circuit to light up the lightbulb. Next the salesperson brought o • 논리 게이트 적용 neutered white female: W13년 2월 3일 일요일 M N
3. 3. 논리식을 이용한 회로의 간략화 104 Chapter Elev Due to the plethora of parentheses, this expression hardly looks simplifie (M x N x (W + T))But there’s N x (1variable in this expression, which means there’s one le + (F x one less - W)) + B switch in the network. Here’s the revised version: W M AND의 순서를 변경 N T (N x M x (W + T)) + (N X F X (1 - W)) + B F W B 배분법칙을 적용 N x (M x (W + T) + F x (1 - W)) + B Indeed, it’s probably 1개의 스위치가 network is equivalent to the e easier to see that this 감소 (N) lier one than to verify that the expressions are the same. Actually, there are still three too many switches in this network. In theo you need only four switches to define your perfect cat. Why four? Ea switch is a bit. You should be able to get by with one switch for the sex (o for male, on for female), another switch that’s on for neutered, off f unneutered, and two more switches for the color. There are four possib colors (white, black, tan, and “other”), and we know that four choices c13년 2월 3일 일요일 be defined with 2 bits, so all you need are two color switches. For examp
4. 4. lors (white, black, tan, and “other”), and we know that four choices can defined with 2 bits, so all you need are two color switches. For exampleoth switches can be off for white, one switch on for black, the other switchn for tan, and both switches on for other colors. Let’s make a control panel right now for choosing a cat. The control pane 이런 장치를 만들수 없을까? have on your wall simply four switches (much like the on/off switches you r controlling your lights) and a lightbulb mounted in a panel: Dream Kitty F N O B T Meow M U W Control Panelhe switches are on (closed) when they’re up, and off (open) when they’reown. The two switches for the cat’s color are labeled somewhat obscurely 13년 2월 3일 일요일
5. 5. 어떤점이 문제인가? 104 Chapter Eleven 스위치를 이용한 전자 회로는 결과 같이 참이 되게 하는 입력 값을 필요 Due to the plethora of parentheses, this expression hardly looks simplified. But there’s one less variable in this expression, which means there’s one less switch in the 하얀색 고양이: W, revised version: 고양이: 1- W ex) network. Here’s the 하얀색이 아닌 W M T N F W B13년 2월 3일 일요일
6. 6. 어떤점이 문제인가? 104 Chapter Eleven 스위치를 이용한 전자 회로는 결과 같이 참이 되게 하는 입력 값을 필요 Due to the plethora of parentheses, this expression hardly looks simplified. But there’s one less variable in this expression, which means there’s one less switch in the 하얀색 고양이: W, revised version: 고양이: 1- W ex) network. Here’s the 하얀색이 아닌 W M T N F W B13년 2월 3일 일요일
7. 7. 어떤점이 문제인가? 104 Chapter Eleven 스위치를 이용한 전자 회로는 결과 같이 참이 되게 하는 입력 값을 필요 Due to the plethora of parentheses, this expression hardly looks simplified. But there’s one less variable in this expression, which means there’s one less switch in the 하얀색 고양이: W, revised version: 고양이: 1- W ex) network. Here’s the 하얀색이 아닌 W M T N F W B 전구에 불이 들어 오기 위해서는 1 - W 스위치가 별도로 필요13년 2월 3일 일요일
8. 8. When an incoming current triggers the electromagnet, the electromagnet pulls down a flexible strip of metal that acts like a switch to turn on an 6장의 릴레이를 활용해 보자 outgoing current: V 릴레이도 병렬 혹은 직렬로 연결되어 간단한 논리 동작 수행 가능할 것 In Out 릴레이는 손가락 대신 전기 신호를 이용해서 스위치를 제어할 수 있음 So a telegraph key, a relay, and a sounder are connected more or less like this: V V Your telegraph The relay station Your friend’s station telegraph station13년 2월 3일 일요일
9. 9. ple functions in arithmetic. Indeed, the next chapter will demonstrate howwire switches, lightbulbs, a battery, and telegraph relays to make an addingchine (albeit one that works solely with binary numbers).As you recall, relays were crucial to the workings of the telegraph system.er long distances, the wires connecting telegraph stations had106 a very high Chapter E stance. Some method was needed to receive a weak signal and send anntical strong signal. The relay did this by using an electromagnet to control 릴레이를 이용한 회로망witch. In effect, the relay amplified a weak signal to create a strong Notice that the switch at the left is open and the lightbulb is off. Wh signal.For our purposes, we’re not interested in using the relay to amplify a weak switch, the battery at the left causes current to flow throu close the many turns of wire around the iron bar. The iron bar becomes magnenal. We’re interested only in the idea of a relay being a switch that can pulls down a flexible metal contact that connects the circuit to turncontrolled by electricity rather than by fingers. We can wire a relay withwitch, a lightbulb, and a couple of batteries like this: lightbulb: 스위치 온 When the electromagnet pulls the metal contact, the relay is said to b gered. When the switch is turned off, the iron bar stops being magnet the metal contact returns to its normal position. This seems like a rather indirect route to light the bulb, and indee If we were interested only in lighting the bulb, we could dispense w relay entirely. But we’re not interested in lighting bulbs. We have a more ambitious goal. We’re going to be using relays a lot in this chapter (and then hardl after the logic gates have been built), so I want to simplify the diagra 13년 2월 3일 일요일 can eliminate some of the wires by using a ground. In this case, the gr
10. 10. but I knowthe diagrams in like achapter, all the we’re not done yet. No- in all this doesn’t look this simplification, but When the electromagnet pulls the metal contact, the relay is said to be trig-that the negative terminals of both batteriesV’s can be connected to one another and all the grounds can be connected to one another.ground. net- tice gered. When the switch is turned off, the iron bar stops being magnetic,So anywhere we see something like this: and are connected to All the the metal contact returns to its normal position. works of relays and logic gates in this chapter and the next will require only one battery, although it might need to be a big battery. For example, the pre- This seems like a rather indirect route to light the bulb, and indeed it is. If we were interested only in lighting the bulb, we could dispense ceding diagram can be redrawn with only one battery like this: with the more ambitious goal. 간단히 표현해 보자 relay entirely. But we’re not interested in lighting bulbs. We have a much We’re going to be using relays a lot in this chapter (and then hardly at all after the logic gates have been built), so I want to simplify the diagram. We can eliminate some of the wires by using a ground. In this case, the grounds simply represent a common connection; they don’t need to be connected to replace it with the capital letter V (which stands for voltage), as we did let’s the physical earth: in Chapters 5 and 6. Now our relay looks like this: 공통 연결 생략 V 108 Chapter Eleven V These diagrams of the relay show two voltage sources and two grounds, but in all the diagrams in this chapter, all the V’s can be connected to one 전지 축약 another and all the grounds can be connected to one another. All the net- works of relays and logic gates in this chapter and the next will require only what we need to do with relays, this diagram isn’t very clear. It’s better But for one battery, although it might need to be a big battery. For example, the pre- to avoid the circular circuits and look at the relay—like the control panel ceding diagram can be redrawn with only one battery like this: earlier—in terms of inputs and outputs: 하나의 전지만switch is closed, a current flows between V and ground through When the 사용 the coils of the electromagnet. This causes the electromagnet to pull the flex- V ible metal contact. That connects the circuit between V, the lightbulb, and ground. The bulb lights up: “Output” or “Out” “Input” or “In” V 전지 및 전구 V 축약 But for what we need to do with relays, this diagram isn’t very clear. It’s better If a current is flowing through the input (for example, if a switch connects to avoid the circular circuits and look at the relay—like the control panel earlier—in terms of inputs and outputs:13년 2월 3일 일요일 the input to V), the electromagnet is triggered and the output has a voltage.
11. 11. 근데 릴레이로 어떤 일을 할 수 있는거야?13년 2월 3일 일요일
12. 12. Gates (Not Bill) 109 논리 게이트 The input of a relay need not be a switch, and the output of a relay need not be a lightbulb. The output of one relay can be connected to the input of another relay, for example, like this: 릴레이를 연결하여 조합 V V V 릴레이를 연결하는 것은 When you turn the switch on, the first relay is triggered, which then pro- vides a voltage to the second relay. The second relay is triggered and the light goes on: 논리 게이트의 가장 중요한 개념13년 2월 3일 일요일
13. 13. 그래서 어떻게 조합하면 되는 거야?13년 2월 3일 일요일
14. 14. V V110 Chapter Eleven 그러기 전에, 릴레이를 조금 다르게 바꿔보자 just as well use the upper contact. When we use this contact, the output of the relay is reversed and the lightbulb is on when the input switch is open: input switch is closed, the bulb goes out: And when the V V 스위치 온 V V And when the input switch is closed, the bulb goes out: Using the terminology of switches, this type of relay is called a double-throw 쌍투 릴레이(Double Throw)are electrically opposite—when one has a relay. It has two outputs that voltage, the other doesn’t. 전기적으로 반대의 특성을 가지는 2개의 a tough time visualizing what modern relays By the way, if you’re having 출력을 가짐 V look like, you can see a few in conveniently transparent packaging at your local Radio Shack. Some, like the heavy-duty relays with Radio Shack part numbers 275-206 and 275-214, are about the size of ice cubes. The insides V are encased in a clear plastic shell, so you can see the electromagnet and the metal contacts. The circuits I’ll be describing in this chapter and the next13년 2월 3일 일요일 could be built using Radio Shack part number 275-240 relays, which are
15. 15. V V110 Chapter Eleven 그러기 전에, 릴레이를 조금 다르게 바꿔보자 just as well use the upper contact. When we use this contact, the output of the relay is reversed and the lightbulb is on when the input switch is open: input switch is closed, the bulb goes out: And when the V V 스위치 온 V V 1-W 스위치 불필요 And when the input switch is closed, the bulb goes out: Using the terminology of switches, this type of relay is called a double-throw 쌍투 릴레이(Double Throw)are electrically opposite—when one has a relay. It has two outputs that voltage, the other doesn’t. 전기적으로 반대의 특성을 가지는 2개의 a tough time visualizing what modern relays By the way, if you’re having 출력을 가짐 V look like, you can see a few in conveniently transparent packaging at your local Radio Shack. Some, like the heavy-duty relays with Radio Shack part numbers 275-206 and 275-214, are about the size of ice cubes. The insides V are encased in a clear plastic shell, so you can see the electromagnet and the metal contacts. The circuits I’ll be describing in this chapter and the next13년 2월 3일 일요일 could be built using Radio Shack part number 275-240 relays, which are
16. 16. 104 Chapter El 쌍투 릴레이를 어떻게 적용하지? Due Chapter Eleven to the plethora of parentheses, this expression hardly looks simpli But there’s one less variable in this expression, which means there’s one switch in the network. Here’s the revised version: st as well use the upper contact. When we use this contact, the output ofhe relay is reversed and the lightbulb is on when the input switch is open: W M T V N F W V Bnd when the input switch is closed, the bulb goes out: Indeed, it’s probably easier to see that this network is equivalent to the lier one than to verify that the expressions are the same. V Actually, there are still three too many switches in this network. In th you need only four switches to define your perfect cat. Why four? E V switch is a bit. You should be able to get by with one switch for the sex 13년 2월 3일 일요일 for male, on for female), another switch that’s on for neutered, of
17. 17. 104 Chapter El 쌍투 릴레이를 어떻게 적용하지? Due Chapter Eleven to the plethora of parentheses, this expression hardly looks simpli But there’s one less variable in this expression, which means there’s one switch in the network. Here’s the revised version: st as well use the upper contact. When we use this contact, the output ofhe relay is reversed and the lightbulb is on when the input switch is open: W M T V N F W V Bnd when the input switch is closed, the bulb goes out: 스위치를 이용한 회로에 바로 적용이 불가능. AND, OR를 위한 새로운 회로 필요 that this network is equivalent to the Indeed, it’s probably easier to see lier one than to verify that the expressions are the same. V Actually, there are still three too many switches in this network. In th you need only four switches to define your perfect cat. Why four? E V switch is a bit. You should be able to get by with one switch for the sex 13년 2월 3일 일요일 for male, on for female), another switch that’s on for neutered, of
18. 18. V Gates (Not Bill) 111 112 Chapter Eleven This bulb 111 light up only if all three switches are closed. Only if the top will 릴레이를 직렬로 연결해 보자 Gates (Not Bill) Just as two switches can be connected in series, two relays can be con- two switches are closed Still thethe output of the first AND switch is still open and first will lightbulb doesn’t light because the bottom gate trigger the Just as two switches can be connected in series, two relays can bein the second AND gate. The bottom switch triggers the second relay relay con- nected in series: that relay isn’t triggered. We can try opening the top switch and closing the bottom switch: nected in series: V in the second AND gate. V If we think of the absence of a voltageVas a 0, and the presence of a volt- V age as a 1, the output of the AND gate is dependent on inputs like this: V V 0 1 0 0 0 0 V V V 0 1 0 1 1 1 112 Chapter Eleven The output of the top relay supplies a voltage to the second relay. As you Still the lightbulb doesn’t light because the bottom switch is still open and is still not lit. The current can’t reach the lightbulb because The lightbulb can see, when both switches are open, the lightbulb isn’t lit. We can try clos- that relay isn’t triggered. We can try opening the top switch and closing the isn’t triggered. The only way to get the bulb to light up is to the first relay ing the top switch: close both switches: The output of the top relay supplies a voltage to the second relay. As you bottom switch: can see, when both switches are open, the lightbulb isn’t lit. We can try clos- ing the V switch: top V V V V V V V V V V V The lightbulb is still not lit. The current can’t reach the lightbulb because the first relay isn’t triggered. The only way to get the bulb to light up is to close both switches: V13년 2월 3일 일요일
19. 19. Gates (Not Bill) 113 Gates (Not Bill) Now both relays are triggered, and current can flow between V, the lightbulb,Now both ground. are triggered, and current can flow between V, the lightbulb, and relaysand ground. the two switches wired in series, these two relays are are triggered. Like little exercise in logic. The bulb lights up only if both relays performing a Like the two switches wired in as an AND these avoid ex- These two relays wired in series are known series, gate. To two relays are performing a cessive drawing, electrical engineers have a special symbol for an AND gate.little exercise inlooks like this: bulb lightswith the if both relays are triggered. That symbol logic. The As up only two switches wired in series, the AND gate can also be desThese two relays wired in series are known as an AND gate. To avoid ex-AND 게이트 in this little table:cessive drawing, electrical engineers have a special symbol for an AND gate. Inputs OutputThat symbol looks like this: This is the first of four basic logic gates. The AND gate has two inputs (at the left in this diagram) and one output (at the right). You’ll often see the AND 0 1 AND gate drawn as this one is with the inputs at the left and the output at the right. That’s because people who are accustomed to reading from left to Inputs right also like to read electrical diagrams from left to right. ButOutput the AND 0 0 0 gate can just as well be drawn with the inputs at the top, the right, or the bottom. The original circuit with the two relays wired in series with two switches 1 0 1 and a lightbulb looked like this: 114 Chapter ElevenThis is the first of four basic logic gates. The AND gate has two inputs (atthe left in this diagram) Vand one output (at the right). You’ll often see theAND gate drawn as this one is with the inputsUsing the symbol for the ANDgatesthis same circuit lookstwo this: It’s also possible to make output at with more than like inputs. F at the left and the AND gate,the right. That’s because people who are accustomed you connect three to ample, suppose to reading from left relays in series: Vright also like to read electrical diagrams from left to표현 But the AND 축약 right.gate can just as well be drawn with the inputs at the top, the right, or the Vbottom. V The original circuit with the two relays wired in series with two switches Vand a lightbulb looked like this: V V V Notice that this symbol for the AND gate not only takes the place of two relays wired in series, but it also implies that the top relay is connected to a voltage, and both relays are connected to ground. Again, the lightbulb lights up only if both the top switch and the bottom switch are closed. That’s why V it’s called an AND gate. The inputs of the AND gate don’t necessarily have to be connected to V switches, and the output doesn’t necessarily have to be connected to a13년 2월 3일 일요일
20. 20. Gates (Not Bill) 115 V As with the two switches wired in series, the AND gate can also be described in this little table: 세개의 입력을 가진 AND 게이트 AND 0 0 0 1 0 1 0 1 It’s also possible to make AND gates with more than two inputs. For ex- ample, suppose you connect three relays in series: V The lightbulb lights up only if all three switches are clo tion is expressed by this symbol: V V V It’s called a 3-input AND gate. The lightbulb lights up only if all three switches are closed. This configura- tion is expressed by this symbol:13년 2월 3일 일요일 It’s called a 3-input AND gate.
21. 21. OR gate. Electrical engineers use a symbol for the OR gate that looks like th Inputs Output It’s somewhat similar to the symbol for the AND gate except that the inp 116 릴레이를 병렬로 연결 side is rounded, much like the O in OR. (That might help you to keep th Chapter Eleven straight.) The output of the OR gate supplies a voltage if either of the two inp The next logic gate involves two relays that are wired in parallel like this: Gates (Not Bill) 117 has a voltage. Again, if we say that the absence of a voltage is 0 and the pr V enceSimilarly, voltage is 1, the OR close the bottom four the of a if we leave the top switch open but gate has switch, possible states: bulb lights up: V V 0 1 0 1 V 0 0 V V V 0 1 1 1 V 1 1 Gates (Not Bill) In the same way that we summarized the output of the AND gate, we c 117 summarize the output of the OR gate: Similarly, if we leave the top switch open but close the bottom switch, the bulb lights up: that the outputs of the two relays are connected Notice to each other. also lights if both switches are closed: The bulb This connected output then provides power for the lightbulb. Either one of the OR 0 1 two relays is enough to light the bulb. For example, if we close the top switch,V V the bulb lights up. The bulb is getting power from the left relay. 0 0 1 V V V 1 1 1 V V V OR gates can also have more than two inputs. (The output of such a gat V 1 if any of the inputs are 1; the output is 0 only if all the outputs are 0. V Earlier I explained how the relays that we’re using are called double-thr V relays because an output can be connected two different ways. Norma the bulb isn’t lit when the switch is open: V The bulb also lights if both switches are closed: V V13년 2월 3일 일요일
22. 22. 0 1 0 0 0 1 OR 게이트 1 1 1 18 Chapter Eleven In the same way that we summarized the output of the AND gate, w What we have here is a situation in which the bulb lights up ifORtop switch summarize the output of the the gate: or the bottom switch is closed. The key word here is or, so this is called the OR gate. Electrical engineers use a symbol for the OR gate that looks like this: OR 0 1 Inputs Output 0 0 1 1 1 1 It’s somewhat similar to the symbol for the AND gate except that the input side is rounded, much like the Ogates can also have more than two inputs. (The output of such a OR in OR. (That might help you to keep them straight.) 1 if any of the inputs are 1; the output is 0 only if all the outputs ar The output of the OR gate supplies a voltage if either of the two inputs Earlier I explained how the relays that we’re using are called double- has a voltage. Again, if we say that the absence of a voltage is 0 and the pres- ence of a voltage is 1, the OR gate because possible states: be connected two different ways. Nor relays has four an output can the bulb isn’t lit when the switch is open: 0 1 0 1 0 0 V13년 2월 3일 일요일 0 1
23. 23. V Gates (Not Bill) 119 When the switch is closed, the bulb lights up. 인버터 Alternatively, you can use the other contact so that the bulb is lit when the switch is open: In this case, the lightbulb goes out when you close the switc In this case, the lightbulb goes out when you close an inverter. An inverter isn’t a lo lay wired in this way is called the switch. A single re- lay wired in this way is called an inverter. An or more inputs), but it’s often very u gates always have two inverter isn’t a logic gate (logic gates always haveless. It’smore inputs), but it’sspecial symbol that looks like this: two or represented by a often very useful nonethe- V less. It’s represented by a special symbol that looks like this: V Input Input Output Output It’s called an inverter called an inverts 0 (no voltage) inverts 0 (noand It’s because it inverter because it to 1 (voltage) voltage) to 1 vice versa: vice versa: In this case, the lightbulb goes out when you close the switch. A single re- lay wired in this way is called an inverter. An inverter isn’t a logic gate (logic 0 gates always have two or more inputs), but it’s often very useful nonethe- 1 less. It’s represented by a special symbol that looks like this: 0 1 Input 1 Output 0 1 0 It’s called an inverter because it inverts 0 (no voltage) to 1 (voltage) and vice versa: With the inverter, the AND gate, and the OR gate, we can start wiring the control panel to automate a choice of the ideal kitty. Let’sand the OR gate, we ca With the inverter, the AND gate, begin with the13년 2월 3일 일요일 0 1
24. 24. 그럼 다시 고양이 회로망으로 ...13년 2월 3일 일요일
25. 25. 0 1 1 0 120 Ch he inverter, the AND gate, and the OR gate, we can start wiringol panel to automate a choice of the ideal kitty. 고양이의 표현 성별과 중성화된 Let’s begin with the When F is 1, M will be 0 and vice versa. Similarly, the second sw The first switch is closed for female and open for male. Thus we for a neutered cat and open for an unneutered cat:rate two signals that we’ll call F and M, like this: V V F N M U 성별next two switches are more complicated. In various c The 중성화 these switches must indicate four different colors. Here are the both wired to a voltage: V 13년 2월 3일 일요일
26. 26. if not:The next two switches are more complicated. In various combinations, e switches must indicate four different colors. Here are the two switches,h wired to a voltage: V Gates (Not Bill) 121 V W V Similarly, if the second switch is closed, we want a tan cat: V 색상의 both inverters are 0. The outputs When the switches are open, the inputs to V 표현 of the inverters (which are inputs to the AND gate) are thus both 1. That means the output indicate the color(Not Bill) of the switches is closed, Gates 1. If eitheren both switches are open (as shown), they of the AND gate is white. V T the output AND gate to gate will be a 0. I’lle’s how to use two inverters and one of the AND generate a signalot: 2개의 Bit를 사용하여 4가지를 표현 가능 To indicate a black cat, we close the first switch. This can be realized using W, which is a voltage (1) if you select a white cat and not a voltage (0) And if one inverter andclosed, we gate: aSimilarly, if the second switch is closed, we want a tan cat: both switches are an AND want cat of an “other” color: V V V V V O B V W V V T Now let’s combine all four little circuits into one big circuit. (As usual, 하얀색 검정색 황갈색en the switches are open, the inputs to both inverters between be outputsifcircuit; wiresclosed, closed anda cat of an “other” color: the black dots indicate connections are will wiresonlyswitches are that is we want The output of the AND gate 0. The 1 in the the first switch And if both cross without blackswitch isnot connected.) 1. That dots are open.thus bothhe inverters (which are inputs second AND gate) are the to the ns the output of the AND gate is 1. If either of the switches is closed, V output of the AND gate will be a 0. WTo indicate a black cat, we close the first switch. This can be realized using inverter and an AND gate: V V O B V V T Now let’s combine all four little circuits into one big circuit. (As usu B the black dots indicate connections between wires in the circuit; wires t V O cross without black dots are not connected.) Yes, I know this set of connections now looks very complicated. But if you output of the ANDtrace through very carefully—if you look atis closedinputs to each AND gate gate will be 1 only if the first switch the two and W second 3일 일요일 is open.see where they’re coming from and try to ignore where they’re also going— 13년 2월 switch to
27. 27. if not:The next two switches are more complicated. In various combinations, e switches must indicate four different colors. Here are the two switches,h wired to a voltage: V Gates (Not Bill) 121 V W V Similarly, if the second switch is closed, we want a tan cat: V 색상의 both inverters are 0. The outputs When the switches are open, the inputs to V 표현 of the inverters (which are inputs to the AND gate) are thus both 1. That means the output indicate the color(Not Bill) of the switches is closed, Gates 1. If eitheren both switches are open (as shown), they of the AND gate is white. V T the output AND gate to gate will be a 0. I’lle’s how to use two inverters and one of the AND generate a signalot: 2개의 Bit를 사용하여 4가지를 표현 가능 To indicate a black cat, we close the first switch. This can be realized using W, which is a voltage (1) if you select a white cat and not a voltage (0) And if one inverter andclosed, we gate: aSimilarly, if the second switch is closed, we want a tan cat: both switches are an AND want cat of an “other” color: V V V V V O B V W V V T Now let’s combine all four little circuits into one big circuit. (As usual, 하얀색 검정색 황갈색en the switches are open, the inputs to both inverters between be outputsifcircuit; wiresclosed, closed anda cat of an “other” color: the black dots indicate connections are will wiresonlyswitches are that is we want The output of the AND gate 0. The 1 in the the first switch And if both cross without blackswitch isnot connected.) 1. That dots are open.thus bothhe inverters (which are inputs second AND gate) are the to the ns the output of the AND gate is 1. If either of the switches is closed, V output of the AND gate will be a 0. WTo indicate a black cat, we close the first switch. This can be realized using 4개의 AND게이트와 2개의 인버터로 V inverter and an AND gate: B V 이루어진 2:4 디코더 O V V T 2개의 조합으로 4개의 출력을 나타낼 수 Now let’s combine all four little circuits into one big circuit. (As usu B connections between wires in 1이 발생 the black dots indicate 있으며, 하나의 출력에서만 the circuit; wires t V O cross without black dots are not connected.) Yes, I know this set of connections now looks very complicated. But if you output of the ANDtrace through very carefully—if you look atis closedinputs to each AND gate gate will be 1 only if the first switch the two and W second 3일 일요일 is open.see where they’re coming from and try to ignore where they’re also going— 13년 2월 switch to
28. 28. 122 Chapter Eleven 게이트를 사용한 고양이 회로 The simplified version of the cat-selection expression was (N × ((M × (W + T)) + (F × (1 − W)))) + B For every + sign in this expression, (F x must be an- W)) + B circuit. (M x N x (W + T)) + there N x (1 OR gate in the For every × sign, there must be an AND gate. N M W T F W B The symbols down페이지 논리식의 the circuit diagram are in the same order 앞 the left side of 출력값 as they appear in the expression. These signals come from the switches wired with inverters and the 2-line-to-4-line decoder. Notice the use of the inverter13년 2월 3일 일요일 for the (1 − W) part of the expression.
29. 29. 너무 많은 릴레이가 사용되는거 아냐?13년 2월 3일 일요일
30. 30. 너무 많은 릴레이가 사용되는거 아냐? AND 게이트당 2개의 릴레이13년 2월 3일 일요일
31. 31. 너무 많은 릴레이가 사용되는거 아냐? AND 게이트당 2개의 릴레이 OR 게이트당 2개의 릴레이13년 2월 3일 일요일
32. 32. 너무 많은 릴레이가 사용되는거 아냐? AND 게이트당 2개의 릴레이 OR 게이트당 2개의 릴레이 인버터당 1개의 릴레이13년 2월 3일 일요일
33. 33. 너무 많은 릴레이가 사용되는거 아냐? AND 게이트당 2개의 릴레이 OR 게이트당 2개의 릴레이 인버터당 1개의 릴레이 “원래 그런 것이다”13년 2월 3일 일요일
34. 34. 끝으로, NOR와 NAND에 대해 알아보자 이 게이트들은 릴레이가 동작하지 않을때 전압이 출력되는 특성을 가짐13년 2월 3일 일요일
35. 35. N M W T F W B NOR 게이트 V The symbols down the left side of the circuit diagram are in the same order as they appear in the expression. These signals come from the switches wired with inverters and the 2-line-to-4-line decoder. Notice the use of the inverter for the (1 − W) part of the expression. Now you might say, “That’s a heck of a lot of relays,” and yes, that’s true. 인버터를 직렬로 연결 There are two relays in every AND gate and OR gate, and one relay for each Gates (Not Bill) inverter. I’d say the only realistic response is, “Get used to it.” We’ll be using a lot more relays in the chapters ahead. Just be thankful you don’t actually have to buy them and wire them at home. We’ll look at two more logic gates in this chapter. Both use the output OR과 반대의 the NOR gate is shown in the following table: The output of 출력을 가짐 of the relay that normally has a voltage present when the relay is untriggered. (This is the output used in the inverter.) For example, in this configuration the output from one relay supplies power to a second relay. With both in- puts off, the lightbulb is on: V NOR 0 1 V This behavior is precisely the opposite of0what happens with 0 1 It’s called NOT OR or, more concisely, NOR. This is the s 1 0 0 NOR gate: V This table shows results opposite those of the OR gate, which are 1 if of the two inputs is 1 and 0 only if both inputs are 0. And yet another way to wire two relays is shown here: V It’s the same as the symbol for the OR except with a little cir13년 2월 3일 일요일 V
36. 36. Gates (Not Bill) This behavior is exactly125 V opposite that of the AND gate. This is called NO NAND 게이트 AND or, more concisely, NAND. The NAND gate is drawn just like AND gate but with a circle at the output, meaning the output is the inve The output of the NOR gate is shown in the following table: NOR 0 1 of the AND gate: V 0 1 1 0 0 0 인버터를 병렬로 연결 Inputs Output This table shows results opposite those of the OR gate, which are 1 if either AND와 반대의 출력을 가짐 of the two inputs is 1 and 0 only if both inputs are 0. And yet another way to wire two relays is shown here: The NAND gate has the following behavior: V V NAND 0 1 0 1 1 This behavior is exactly opposite that of the AND gate. This is calle AND or, more concisely, NAND. The NAND gate is drawn just l 1 1 0 AND gate but with a circle at the output, meaning the output is the V of the AND gate: Notice that the output of the NAND gate is opposite the AND gate. The out V of the AND gate is 1 only if both inputs are 1; otherwise, the output is 0 At this point, we’ve looked at four different ways of wiring relays t have two inputs and Inputs Output one output. Each configuration behaves in a sligh different way. To avoid drawing and redrawing the relays, we’ve called th logic gates and decided to use the same symbols to represent them that The NAND gate has the following behavior: In this case, the two outputs are connected, which is similar to the OR configuration but using the other contacts. The lightbulb is on when both switches are open.13년 2월 3일 일요일
37. 37. V used by electrical engineers. The output of the particular logic gate depends on the input, which is summarized here: AND 0 1 OR 0 1 0 1 0 0 0 1 릴레이와 같은 모양의 버퍼 0 1 0 1 1 1 NAND 0 1 NOR 0 1 0 1 1 0 1 0 1 약해진 신호를 증폭, 신호를 지연시키는 용도 1 0 1 0 0 So now we have four logic gates and the inverter. Completing this array of tools is just a regular old relay: This is called a buffer, and this is the symbol for it: V V It’s the same symbol as the inverter but without the little is remarkable for not doing much. The output of the buf This is called a buffer, and this is the symbol for it: the input:13년 2월 3일 일요일
38. 38. mportance of Boole’s insights. He unselfishly encoura cuit that looked like this: configuration like this is drawn without the inverters:d him along the way, and is today sadly almost forgotmous laws. Notice the little circles at the input to the AND gate. Those little circles meanrgan’s Laws are most the signalsversa.inverted at that point—a 0 (no voltage) becomes a 1 (volt- that simply expressed this way: 드모르간의 법칙 are Two inputs are inverted and become inputs to an AND gate. Sometimes a age) and vice configuration like this is drawn without the inverters: An AND gate with two inverted inputs does exactly the same thing as a NOR gate: AxB=A+B = Notice the little circles at the input to the AND gate. Those little circles mean age) and vice versa. A+B=AxB that the signals are inverted at that point—a 0 (no voltage) becomes a 1 (volt- The output is 1 only if both inputs are 0. An AND gate with two inverted inputs does exactlyOR gate with the a Similarly, an the same thing as two inputs inverted is equivalent to a NOR gate: NAND gate: re two Boolean operands. In the first expression, they’r = = combined with the Boolean ifANDareoperator. This is th The output is 1 only if both inputs are 0. The output is 0 only both inputs 1. Similarly, an OR gate with the two inputs inverted is equivalent to a the two operands with De Morgan’s Laws. Augustus DeBoole, whose book Formal Logic tation of the Boolean OR operator and th These two pairs of equivalent circuits represent an electrical implemen- NAND gate: Morgan was another Victorian- 논리식을 간단히 만들어 주기 때문에 era mathematician, nine years older than ult (which is the NOR). In1847,ofthe very Indeed,day (thehad been inspired to investi- the was published in =Mathematical Analysisthe second expression, 중요한 법칙 same story goes) as Boole’s The 회로를 만들때publicLogic.that was Boole waged between De Morgan nverted and then combined with the Boolean OR oper gate logic by a very feud being The output is 0 only if both inputs are 1. e as combining the operands with the Boolean AND op These two pairs of equivalent circuits represent an electrical implemen- tation of De Morgan’s Laws. Augustus De Morgan was another Victorian- era mathematician, nine years older than Boole, whose book Formal Logic ting (which is the NAND). was published in 1847, the very same day (the story goes) as Boole’s The 13년 2월 3일 일요일