Vi G V0
L
H
L
H L
L
H
H Open
Open
L
H
Fig 1-9 A tri-state buffer.(a) Model. (b) Truth table.(c) Symbol.
Since the buffer is capable of delivering additional current to a load, it is often called buffer amplifier
a buffer amplifier The traditional amplifier symbol (a triangle) shown in Fig. 1-8c is used tri-state buffer
on schematic diagrams. If you ‘ re interested in an actual IC buffer , look in the standard enable input
TTL logic family . The 5407 or 7407 is a 14-pin IC that contains six buffers. Inversion
THE TRI STATE BUFFER inverter
At the input of a digital system , there may be more than one input signal of interest. NOT circuit
Generally speaking, however , it will be necessary to connect only one signal at a time, and thus there is a requirement to connect or disconnect (switch) input signals electronically. Similarly, the output of a digital system may need to be directed to more than one destination, one at a time.
The logic circuit in Fig. 1-9 a is a simple buffer with an additional switch controlled by an input labeled G. When G is low, this switch is open and the output is ‘’disconnected’’ from the buffer. When G is closed and the output follows the input. That is, the circuit behaves as ordinary buffer amplifier. In effect, the control signal G connects the buffer to the load or disconnects the. Buffer from the load.
The truth table in Fig. 1-9b summarizes circuit operation. Notice that hen G is high, V0 is ether high or low (two states). However ,when G s lo, the output is in effect an open circuit (a third state!). Since there are three possible states For V0, this circuit is called a tri-state buffer.(Tri stands for “three” and thus the tern three-state buffer is often used.)
The standard symbol for a tri-state buffer such as this is shown in Fig.1-9c.It is simply the buffer symbol with an additional input ,G. Since G controls operation of the circuit, it is often referred to as the enable input. In the standard TTL logic family ,a 54126 or a 74126 is a14-pin IC that has four of these circuits.
THE INVERTER
One of the most basic operations in a digital system is inversion, or negation. This Requires a circuit that will invert a digital level. This logic circuit is called an inverter, or sometimes a NOT circuit. The switch arrangement in Fig. 1-10a is an inverter. When the input to this circuit is low, the switch remains up and the output is high. When the input is high, the switch moves down and the output is low. The truth for the inverter is
Vi V0
L
H H
L
Fig. 1-10 Digital inverter. (a) Model. (b) Truth table. (c) Symbol. (d) Another symbol.
Negation given in Fig. 1-10b. Clearly the output is the negative, or the inverse, of the input.
Tri- state inverter When the inverter is used as a logic circuit, H is often defined as the ‘’true’’ state, while L is defined as the ‘’false’’ state In this state ,the inverter will always provide at its output a signal that is the inverter. Or complement, of the signal at input. It is thus called a negation or NOT circuit. This makes sense, since there are only two possible states, and therefore NOT H must be L and must be H.
The inverse or complement of a signal is shown by writing a bar above the symbol. For instance , the complement of A is written as ¯A ,and this is read as ‘’ A bar.’’ A logic expression for the inverter in Fig. 1-10c is V0 =V ̅i. It is read ‘’V sub oh is equal to V sub eye bar.’’
The standard symbol for an inverter is given in Fig. 1-10c. Notice the small circle (bubble) at the output. This small circle signifies inversion, and it is used on many other logic symbols. For instance, the symbol in Fig. 1-10d has the small circle on the input side. This is still an inverter, but the circle on the input side has additional significance. which will be considered next. In the standard TTL logic family, a 5404 or7404 s a 14-pin IC with six inverters.
THE TRI –STATE INVERTER
A tri-sate inverter is easy to construct, as shown in Fig. 1-11a. The truth table in Fig. 1-11b shows that when G is low, the inverter is connected to output. When G is high the enable switch open, and the output is disconnected from the inverter. The standard logic symbol for this tri-state inverter s giver in Fig. 1-11c. The inverting amplifier Symbol indicates that V0 is the inverse of Vi (the small circle is at the amplifier output). However, note small circle at the input of the amplifier used for G. From the truth
Vi G V0
L
H
L
H L
L
H
H L
H
Open
Open
Fig. 1-11 Inverting tri-state buffer. (a) Model. (b) Truth table. (c) Symbol
table , you can see that the switch controlled by G is closed hen G is low! Thus, wen G AND gate
is low, the circuit is activated and output v0 is the inverse of the input vi Compare this
with the G input to the tri-state buffer in Fig. 1-9. In this case, the switch is closed and
the circuit is activated when G is high. Here, then ,is the significance of the circle on
the input side: Placing a circle at the input of a logic circle is activated when the signal
at that input is low! The tri-state inverters used on the 74LS386A IC (TTL logic family)
are similar to FIG. 1-11.
THE AND GATE
An AND gate is a digital circuit having two or more input and a single output as indicated in Fig. 1-12. The inputs to this gate are labeled V1,V2, V3,…VN(there are input), and the output is labeled V0. The operation of an AND gate can be expressed in a number of different, but equivalent, ways. For instance,
If any input is low, V0 will be low.
2. V0 will be high only when all input are high.
3. V0 = H only if V1 = H, and V2 = H, and V3 = H, . . . and Vn = H.
This last statement leads to the designation AND gate, since V1 and V2, and V3, . . . and Vn must all be high in order for V0 to be high.
Fig. 1-12 AND gate.
A model for an AND gate having 2 input is shown in Fig. 1-13a . This gate can be used to make ‘’ logical’’ decisions; for example. ‘’ If V1 and V2 then V0 ‘’ As result, it is referred to as a digital logic circuit, as are all AND gates. From the model, it is seen that V1 = H closes the upper switch, and V2 =H closes the lower switch. Clearly, V0 = H only when both V1 and V2 are high. This can be expressed in of from of a logic equation written as
V0 = V1 AND V2
V1 V2 V0
L
H
L
H L
L
H
H L
L
L
H
Fig. 1-13 Two-input AND gate. (a) Model. (b) Truth table. (c) Symbol.
Fig. 1-14 OR gate.
The operation is summarized in the truth table in Fig. 1-13b. The symbol for a 2-input AND gate is shown in Fig 1-13c.
THE OR GATE
An OR gate is also a digital circuit having 2 or more inputs and a output as indicated in Fig. 1-14. The input to this gate are labeled 1, V2, V3, . . . .Vn (there are n input), and the output is labeled V0.The operation of an OR gate can be expressed in a number of different ways. For instance,
1.V0 will be low only when all input are low.
2. If any input is high, V0 will be high.
3. V0 = H if V1, or V2, or V3, . . . or Vn = H.
This last statement leads to the designation OR gate, since V0 = H only if V1 or V2 or V3, . . . Vn = H.
A model for an OR gate having 2 input is shown in Fig. 1-15a. This gate can be used to make ‘’ logical ‘’ decisions; for example, ‘’ If V1 or V2 then, V0. ‘’ As result, it is referred to as a digital logic circuit, as are all OR gates. From the model, it is seen that V1 = H closes the upper switch, and V2 = H closes the lower switch. Clearly, V0 = H either V1 or V2 is high. This can be expressed in the form of a ‘’ logic’’ equation written as
V0 = V1 OR V2
The operation is summarized in the truth table in Fig. 1-15b. The symbol for a 2-input OR gate s shown in Fig 1-15c.
V1 V2 V0
L
H
L
H L
L
H
H L
H
H
H
Fig. 1-15 Two-input OR gate. (a) Model. (b) Truth table. (c) Symbol.
9. Refer only to the tri-state buffer symbol in Fig. 1-9c determine the state of V0 f both G and Vi are low. Check your response with the truth in Fig 1-9b. Repeat if both G and Vi are high.
10. Refer only to the inverting tri-state buffer symbol in. 1-11c and determine the state of V0 if both G and Vi are low . Check your response with the truth table in Fig. 1-11b. Repeat if both G and vi are high
11.For the AND gate in Fig. 1-13c, V1 = H and V2 = L. What is the state of V0?
12. If the AND gate in Fig. 1-13c had an additional input (V3), and V1 = V2 = H, and V3 = L, what would be the state of V0? What would it take to produce V0 = H?
13. If the OR gate in Fig. 1-15c had an additional input (V3), and V1 = V2 =V H, and V3 = L, what would be the sate of V0? What would it take to produce V0 = L?
1-4 MOVING AND STORING DIGITAL INFORMATION
MEMORY ELEMENTS
A digital memory element is a device or perhaps a circuit that will maintain a desired logic level at its output. The simplest memory element is the switch in Fig 1-17a and b. The switch in Fig 1-7a is placed such that its output is low, and it will remain low without any further action. Thus, it will ‘’remember’’ that V0 = L. Since L = 0 = 0 Vdc, the switch can be thought of as ‘’holding’’ or ‘’storing’’ a logic 0. In Fig. 1-7b, V0 =H, and it will remain high without any further action. The switch remembers that V0 = H. In this case, the switch is can be used to store a digital level, and it will remember the stored level indefinitely.
The simplest electronic circuit used as a memory element is called a
Vi G V0LHLH LLHH OpenOpenLH Fig 1-9 A tri-state buffer.(a) Model. (b) Truth table.(c) Symbol. Since the buffer is capable of delivering additional current to a load, it is often called buffer amplifiera buffer amplifier The traditional amplifier symbol (a triangle) shown in Fig. 1-8c is used tri-state bufferon schematic diagrams. If you ‘ re interested in an actual IC buffer , look in the standard enable input TTL logic family . The 5407 or 7407 is a 14-pin IC that contains six buffers. InversionTHE TRI STATE BUFFER inverterAt the input of a digital system , there may be more than one input signal of interest. NOT circuitGenerally speaking, however , it will be necessary to connect only one signal at a time, and thus there is a requirement to connect or disconnect (switch) input signals electronically. Similarly, the output of a digital system may need to be directed to more than one destination, one at a time. The logic circuit in Fig. 1-9 a is a simple buffer with an additional switch controlled by an input labeled G. When G is low, this switch is open and the output is ‘’disconnected’’ from the buffer. When G is closed and the output follows the input. That is, the circuit behaves as ordinary buffer amplifier. In effect, the control signal G connects the buffer to the load or disconnects the. Buffer from the load. ตารางความจริงใน Fig. 1 9b สรุปวงจรการดำเนินงาน สังเกตว่า ไก่ G สูง V0 คือ อีเทอร์สูง หรือต่ำ (สองอเมริกา) อย่างไรก็ตาม เมื่อ G s หล่อ ผลผลิตได้ผลเป็นวงจรเปิด (สามรัฐ) เนื่องจากมีสามสถานะได้สำหรับ V0 วงจรนี้เรียกว่าบัฟเฟอร์ตรีรัฐ (ตรีถึง "สาม" จึงตื่นสามรัฐบัฟเฟอร์มักใช้) สัญลักษณ์มาตรฐานสำหรับบัฟเฟอร์ตรีรัฐเช่นนี้แสดงใน 9c.It ภาพเป็นเพียงสัญลักษณ์บัฟเฟอร์ ด้วยการป้อนข้อมูลเพิ่มเติม กรัม ตั้งแต่ G ควบคุมการทำงานของวงจร มันมักจะเรียกว่าเข้าเปิดใช้งาน ในมาตรฐาน TTL ตรรกะครอบครัว เป็น 54126 หรือ 74126 เป็น IC a14-pin ที่ 4 ของวงจรเหล่านี้เครื่องแปลงกระแสไฟฟ้าหนึ่งของการดำเนินงานพื้นฐานในระบบดิจิทัลคือกลับ หรือนิเสธ ต้องเป็นวงจรที่จะสลับระดับดิจิตอล วงจรตรรกะนี้จะเรียกว่าเป็นอินเวอร์เตอร์ หรือบางครั้งเป็นวงจรไม่ เรียงสลับใน Fig. 1 10a เครื่องแปลงกระแสไฟฟ้าที่ได้ เมื่ออินพุตให้วงจรนี้มีน้อย สวิตช์ยังคงค่า และผลผลิตสูง เมื่ออินพุตสูง สวิตช์เลื่อนลง และผลผลิตจะต่ำ ความจริงสำหรับเครื่องแปลงกระแสไฟฟ้า Vi V0LH HL เครื่องแปลงกระแสไฟฟ้าดิจิตอล fig. 1-10 (ก) แบบจำลอง (ข) ตารางความจริง (ค) สัญลักษณ์ (d) สัญลักษณ์อีกด้วยปฏิเสธให้ Fig. 1-10 ข ชัดเจนออกคือ การลบ หรือผกผัน ของอินพุตอินเวอร์เตอร์ตรีรัฐเมื่อใช้เครื่องแปลงกระแสไฟฟ้าเป็นวงจรตรรกะ H มักจะถูกกำหนดเป็นรัฐ ''จริง '' ในขณะที่ L กำหนดไว้ ตามรัฐ ''ผิด '' ในสถานะนี้ อินเวอร์เตอร์จะเสมอให้เอาท์พุทของสัญญาณที่เป็นเครื่องแปลงกระแสไฟฟ้า หรือส่วนเติม เต็ม สัญญาณที่ป้อนเข้า จึงเรียกว่านิเสธหรือวงจรไม่ นี้ทำให้รู้สึก เนื่องจากมีอเมริกาได้สองเท่า และดังนั้น H ไม่ต้อง L และต้อง H. ผกผันการของสัญญาณถูกแสดง โดยเขียนแถบเหนือสัญลักษณ์ ตัวอย่าง ส่วนเติมเต็มของ A เขียนเป็น ¯A และนี้คืออ่านเป็น ''บาร์ '' นิพจน์ตรรกะสำหรับอินเวอร์เตอร์ใน Fig. 1-10c เป็น V0 = V ̅i ถูกอ่าน ''ย่อย V โอ้ ได้เท่ากับ V ย่อยตาบาร์"สัญลักษณ์มาตรฐานสำหรับอินเวอร์เตอร์ที่ถูกกำหนดใน Fig. 1-10 c สังเกตวงกลมเล็ก (ฟอง) ที่แสดงผล วงกลมเล็กนี้หมายถึงกลับ และการใช้ในสัญลักษณ์ตรรกะอื่น ๆ มากมาย ตัวอย่าง สัญลักษณ์ใน Fig. 1-10 มีวงกลมขนาดเล็กทางด้านอินพุต นี้ยังคงเป็นอินเวอร์เตอร์ที่ แต่วงกลมทางด้านอินพุตมีความสำคัญเพิ่มเติม ซึ่งจะพิจารณาต่อไป ในมาตรฐาน TTL ตรรกะครอบครัว ความ s 5404 or7404 IC 14 ขากับอินเวอร์เตอร์ 6ตรี – รัฐอินเวอร์เตอร์A tri-sate inverter is easy to construct, as shown in Fig. 1-11a. The truth table in Fig. 1-11b shows that when G is low, the inverter is connected to output. When G is high the enable switch open, and the output is disconnected from the inverter. The standard logic symbol for this tri-state inverter s giver in Fig. 1-11c. The inverting amplifier Symbol indicates that V0 is the inverse of Vi (the small circle is at the amplifier output). However, note small circle at the input of the amplifier used for G. From the truthVi G V0LHLH LLHH LHOpenOpenFig. 1-11 Inverting tri-state buffer. (a) Model. (b) Truth table. (c) Symboltable , you can see that the switch controlled by G is closed hen G is low! Thus, wen G AND gate is low, the circuit is activated and output v0 is the inverse of the input vi Compare this with the G input to the tri-state buffer in Fig. 1-9. In this case, the switch is closed and the circuit is activated when G is high. Here, then ,is the significance of the circle on the input side: Placing a circle at the input of a logic circle is activated when the signal at that input is low! The tri-state inverters used on the 74LS386A IC (TTL logic family) are similar to FIG. 1-11.THE AND GATEAn AND gate is a digital circuit having two or more input and a single output as indicated in Fig. 1-12. The inputs to this gate are labeled V1,V2, V3,…VN(there are input), and the output is labeled V0. The operation of an AND gate can be expressed in a number of different, but equivalent, ways. For instance, If any input is low, V0 will be low. 2. V0 will be high only when all input are high. 3. V0 = H only if V1 = H, and V2 = H, and V3 = H, . . . and Vn = H.This last statement leads to the designation AND gate, since V1 and V2, and V3, . . . and Vn must all be high in order for V0 to be high.Fig. 1-12 AND gate. A model for an AND gate having 2 input is shown in Fig. 1-13a . This gate can be used to make ‘’ logical’’ decisions; for example. ‘’ If V1 and V2 then V0 ‘’ As result, it is referred to as a digital logic circuit, as are all AND gates. From the model, it is seen that V1 = H closes the upper switch, and V2 =H closes the lower switch. Clearly, V0 = H only when both V1 and V2 are high. This can be expressed in of from of a logic equation written as V0 = V1 AND V2V1 V2 V0LHLH LLHH LLLHFig. 1-13 Two-input AND gate. (a) Model. (b) Truth table. (c) Symbol.Fig. 1-14 OR gate.The operation is summarized in the truth table in Fig. 1-13b. The symbol for a 2-input AND gate is shown in Fig 1-13c.THE OR GATEAn OR gate is also a digital circuit having 2 or more inputs and a output as indicated in Fig. 1-14. The input to this gate are labeled 1, V2, V3, . . . .Vn (there are n input), and the output is labeled V0.The operation of an OR gate can be expressed in a number of different ways. For instance, 1.V0 will be low only when all input are low. 2. If any input is high, V0 will be high. 3. V0 = H if V1, or V2, or V3, . . . or Vn = H.This last statement leads to the designation OR gate, since V0 = H only if V1 or V2 or V3, . . . Vn = H.A model for an OR gate having 2 input is shown in Fig. 1-15a. This gate can be used to make ‘’ logical ‘’ decisions; for example, ‘’ If V1 or V2 then, V0. ‘’ As result, it is referred to as a digital logic circuit, as are all OR gates. From the model, it is seen that V1 = H closes the upper switch, and V2 = H closes the lower switch. Clearly, V0 = H either V1 or V2 is high. This can be expressed in the form of a ‘’ logic’’ equation written asV0 = V1 OR V2The operation is summarized in the truth table in Fig. 1-15b. The symbol for a 2-input OR gate s shown in Fig 1-15c.V1 V2 V0LHLH LLHH LHHHFig. 1-15 Two-input OR gate. (a) Model. (b) Truth table. (c) Symbol.9. Refer only to the tri-state buffer symbol in Fig. 1-9c determine the state of V0 f both G and Vi are low. Check your response with the truth in Fig 1-9b. Repeat if both G and Vi are high.10. Refer only to the inverting tri-state buffer symbol in. 1-11c and determine the state of V0 if both G and Vi are low . Check your response with the truth table in Fig. 1-11b. Repeat if both G and vi are high11.For the AND gate in Fig. 1-13c, V1 = H and V2 = L. What is the state of V0?12. If the AND gate in Fig. 1-13c had an additional input (V3), and V1 = V2 = H, and V3 = L, what would be the state of V0? What would it take to produce V0 = H?13. If the OR gate in Fig. 1-15c had an additional input (V3), and V1 = V2 =V H, and V3 = L, what would be the sate of V0? What would it take to produce V0 = L?
1-4 MOVING AND STORING DIGITAL INFORMATION
MEMORY ELEMENTS
A digital memory element is a device or perhaps a circuit that will maintain a desired logic level at its output. The simplest memory element is the switch in Fig 1-17a and b. The switch in Fig 1-7a is placed such that its output is low, and it will remain low without any further action. Thus, it will ‘’remember’’ that V0 = L. Since L = 0 = 0 Vdc, the switch can be thought of as ‘’holding’’ or ‘’storing’’ a logic 0. In Fig. 1-7b, V0 =H, and it will remain high without any further action. The switch remembers that V0 = H. In this case, the switch is can be used to store a digital level, and it will remember the stored level indefinitely.
The simplest electronic circuit used as a memory element is called a
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