数字电路英文版第五单元
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CHAPTER 5 COMBINATIONAL LOGIC
CHAPTER 5 Dual symbol ( 对偶符号 ) Node ( 节点 ) Signal tracing (信号跟踪) Universal gate ( 万能门 ) Combinational logic (组合逻辑) Sequential logic ( 时序逻辑)
AND NOT OR
X=AB (CD + EF)
AND
(a)
A
X=AB (CD + EF)
Biblioteka Baidu
B
C
CD
D
D E
CD+EF
F
EF
13.
X=AB (CD + EF)= ABCD + ABEF
A
B
ABCD
C
D
X=ABCD + ABEF
Signal tracing A troubleshooting technique in which waveforms are observed in a step-by-step manner beginning at the input and working toward the output or vice versa. At each point the observed waveform is compared with the correct signal for that point.
101 1 0 1 110 0 1 0
110 1 1 0
111 0 1 0 111 1 1 1
Output
X
0 0 0 1 0 0 0 1 0 0 0
1 1
1
1 1
AND-OR-Invert Logic ( POS )
A
AB
B
C CD
D
A & ≥1
X
B
X
C&
D
X = AB + CD = (A + B)(C + D)
KAY TERM
Dual symbols The negative-AND is the dual symbol for the NOR gate, and the negative-OR is the dual symbol fot the NAND gate.
Node A common connection point in a circuit in which a gate output is connected to one or more gate inputs.
2.
In this section, the AND—OR and the AND-OR-Invert are examined; and the exclusive-OR and exclusive-NOR gates, which are actually a form of AND-OR logic, are covered.
11.
From a Boolean Expression to a Logic Circuit
Let’s examine the following Boolean expression :
AND
X=AB + CDE
OR
A B
X=AB+CDE
C D E
12.
As another example, let’s implement the following expression :
3.
AND-OR Logic ( SOP )
A B
AB
A & ≥1
XB
X
C
C&
D
CD
D
Fig.5-1
X = AB + CD
4.
TABLE 5-1 Truth table for the AND-OR logic in Fig.5-1
X = AB + CD
5.
Input
A B C D AB CD
000 0 0 0 000 1 0 0 001 0 0 0 001 1 0 1 010 0 0 0 010 1 0 0 011 0 0 0 011 1 0 1 100 0 0 0 100 1 0 0 101 0 0 0
6.
Exclusive-OR Logic
A
AB
XA B
B
AB
A
X = AB+AB
B
=A◯B
X =1
X
7.
X = AB+AB =A◯B
Input
A
B
0
0
0
1
1
0
1
1
Output
X 0 1 1 0
8.
Exclusive-NOR Logic
A X
B
X=AB+AB
XOR
A
AB
B
X
AB
X=AB+AB 9.
§5.1 BASIC COMBINATIONAL LOGIC CIRCUITS
In Chapter 4, you learned that SOP expressions are implemented with an AND gate for each product term and one OR gate for summing all of the product terms. This SOP implementation is called AND—OR logic and is the basic form for realizing standard Boolean functions.
X = AB+AB =AB+AB =A◯B
A
X
B
=1 X
10.
§5.2 IMPLEMENTING COMBINATIONAL LOGIC
In this section, examples are used to illustrate how to implement a logic circuit from a Boolean expression or a truth table. Minimization of a logic circuit using the methods covered in Chapter 4 is also discussed.
Universal gate Either a NAND gate or a NOR gate. The term universal refers to the property of a gate that permits any logic function to be implemented by that gate or by a combination of gates of that kind.
CHAPTER 5 Dual symbol ( 对偶符号 ) Node ( 节点 ) Signal tracing (信号跟踪) Universal gate ( 万能门 ) Combinational logic (组合逻辑) Sequential logic ( 时序逻辑)
AND NOT OR
X=AB (CD + EF)
AND
(a)
A
X=AB (CD + EF)
Biblioteka Baidu
B
C
CD
D
D E
CD+EF
F
EF
13.
X=AB (CD + EF)= ABCD + ABEF
A
B
ABCD
C
D
X=ABCD + ABEF
Signal tracing A troubleshooting technique in which waveforms are observed in a step-by-step manner beginning at the input and working toward the output or vice versa. At each point the observed waveform is compared with the correct signal for that point.
101 1 0 1 110 0 1 0
110 1 1 0
111 0 1 0 111 1 1 1
Output
X
0 0 0 1 0 0 0 1 0 0 0
1 1
1
1 1
AND-OR-Invert Logic ( POS )
A
AB
B
C CD
D
A & ≥1
X
B
X
C&
D
X = AB + CD = (A + B)(C + D)
KAY TERM
Dual symbols The negative-AND is the dual symbol for the NOR gate, and the negative-OR is the dual symbol fot the NAND gate.
Node A common connection point in a circuit in which a gate output is connected to one or more gate inputs.
2.
In this section, the AND—OR and the AND-OR-Invert are examined; and the exclusive-OR and exclusive-NOR gates, which are actually a form of AND-OR logic, are covered.
11.
From a Boolean Expression to a Logic Circuit
Let’s examine the following Boolean expression :
AND
X=AB + CDE
OR
A B
X=AB+CDE
C D E
12.
As another example, let’s implement the following expression :
3.
AND-OR Logic ( SOP )
A B
AB
A & ≥1
XB
X
C
C&
D
CD
D
Fig.5-1
X = AB + CD
4.
TABLE 5-1 Truth table for the AND-OR logic in Fig.5-1
X = AB + CD
5.
Input
A B C D AB CD
000 0 0 0 000 1 0 0 001 0 0 0 001 1 0 1 010 0 0 0 010 1 0 0 011 0 0 0 011 1 0 1 100 0 0 0 100 1 0 0 101 0 0 0
6.
Exclusive-OR Logic
A
AB
XA B
B
AB
A
X = AB+AB
B
=A◯B
X =1
X
7.
X = AB+AB =A◯B
Input
A
B
0
0
0
1
1
0
1
1
Output
X 0 1 1 0
8.
Exclusive-NOR Logic
A X
B
X=AB+AB
XOR
A
AB
B
X
AB
X=AB+AB 9.
§5.1 BASIC COMBINATIONAL LOGIC CIRCUITS
In Chapter 4, you learned that SOP expressions are implemented with an AND gate for each product term and one OR gate for summing all of the product terms. This SOP implementation is called AND—OR logic and is the basic form for realizing standard Boolean functions.
X = AB+AB =AB+AB =A◯B
A
X
B
=1 X
10.
§5.2 IMPLEMENTING COMBINATIONAL LOGIC
In this section, examples are used to illustrate how to implement a logic circuit from a Boolean expression or a truth table. Minimization of a logic circuit using the methods covered in Chapter 4 is also discussed.
Universal gate Either a NAND gate or a NOR gate. The term universal refers to the property of a gate that permits any logic function to be implemented by that gate or by a combination of gates of that kind.