Transcript A + B

Summary
Pp 92 Parity Method
Pp 94 The parity method is a method of error detection for
simple transmission errors involving one bit (or an odd
number of bits). A parity bit is an “extra” bit attached to a
group of bits to force the number of 1’s to be either even
(even parity) or odd (odd parity).
The ASCII character for “a” is 1100001 and for “A” is
1000001. What is the correct bit to append to make both of
these have odd parity?
The ASCII “a” has an odd number of bits that are equal to 1;
therefore the parity bit is 0. The ASCII “A” has an even
number of bits that are equal to 1; therefore the parity bit is 1.
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
PP125 Fig 25 A simplified intrusion detection
system using an OR gate.
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Pp128 Fig.30 Standard symbols representing the two
equivalent operations of a NAND gate.
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Pp128 Fig 31
Floyd, Digital Fundamentals, 10th ed
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Pp 129 Fig32
Floyd, Digital Fundamentals, 10th ed
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Pp129 Fig 33
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Pp 132 Fig 38 Standard symbols representing the two
equivalent operations of a NOR gate.
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Pp133 Fig 40
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Pp134 Fig41
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
5. The symbol
A
B
X
is for a(n)
a. OR gate
b. AND gate
c. NOR gate
d. XOR gate
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
© 2008 Pearson Education
6. A logic gate that produces a HIGH output only when
all of its inputs are HIGH is a(n)
a. OR gate
b. AND gate
c. NOR gate
d. NAND gate
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
© 2008 Pearson Education
7. The expression X = A + B means
a. A OR B
b. A AND B
c. A XOR B
d. A XNOR B
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
© 2008 Pearson Education
8. A 2-input gate produces the output shown. (X represents
the output.) This is a(n)
a. OR gate
b. AND gate
c. NOR gate
d. NAND gate
A
B
X
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
© 2008 Pearson Education
9. A 2-input gate produces a HIGH output only when the
inputs agree. This type of gate is a(n)
a. OR gate
b. AND gate
c. NOR gate
d. XNOR gate
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
© 2008 Pearson Education
10. The required logic for a PLD can be specified in an
Hardware Description Language by
a. text entry
b. schematic entry
c. state diagrams
d. all of the above
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
© 2008 Pearson Education
脈波操作
3-9
pp127/中pp131
若圖3-28所示的A和B兩波輸入NAND閘，則輸出波形為何？
圖3-28
解：在時序圖中，共有4個時間區間A和B輸入波皆為HIGH，只在
這4個時間區段中的輸出波X為LOW。
相關問題 若B輸入波LOW ，則輸出波和時序圖會有何變化？請畫
Floyd, Digital Fundamentals, 10th ed
出來。
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
P131
脈波操作
例3-12
(續)
Pp129/中pp134
圖3-32
要注意的是，此例題與例題3-13中所使用的是相同的2輸
入端NAND閘，但電路圖中卻用了不同的符號，這是為了表示
NAND閘和輸入反相的OR閘用法不同。
相關問題 圖3-32的電路要如何改良才能監控四個儲存槽內的
液體體積？
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
P134
脈波操作
Pp133 Fig 3-47 若B輸入波恒為LOW ，則
輸出波形和時序圖會 變成怎樣？請畫出來
若B輸入波恒為 High?
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
P144
以同位法檢測錯誤
由表2-10列出每個BCD數
表2-10
偶
同
位
奇
同
位
要形成偶或奇同位所須的同位
P
BCD
P
BCD
位元，可以看出在數碼上附加
0
0000
1
0000
同位位元的方法。各個BCD數
1
0001
0
0001
1
0010
0
0010
0
0011
1
0011
1
0100
0
0100
0
0101
1
0101
的開頭或末端，端視系統的設
0
0110
1
0110
1
0111
0
0111
計而定。注意1的總數 ( 包含
1
1000
0
1000
0
1001
1
1001
的同位位元列在標示P的欄中。
同位位元可以附加在代碼
同位位元在內 ) 在偶同位時要
恆為偶數，在奇同位時則要恆
為奇數。
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
P097
以同位法檢測錯誤
2-34
對下列各位元組指定一個適當的偶數同位位元：
(a)1010
(b)111000
(d)100011100101
(c)101101
(e)101101011111
解：視情形在各代碼中加入同位位元1或0，使整個代
碼中1的個數為偶數。同位位元在最左邊。
(a)01010
(b)1111000
(d)0100011100101
(c)0101101
(e)1101101011111
相關問題 在代表字母K的7位元ASCII碼加入一個奇
同位位元。
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
P098
Summary
Boolean Multiplication
Pp180 In Boolean algebra, multiplication is equivalent to the
AND operation. The product of literals forms a product term.
The product term will be 1 only if all of the literals are 1.
What are the values of the A, B and C if the
product term of A.B.C = 1?
Each literal must = 1; therefore A = 1, B = 0 and C = 0.
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Commutative Laws
The commutative laws are applied to addition and
multiplication. For addition, the commutative law states
In terms of the result, the order in which variables
are ORed makes no difference.
A+B=B+A
For multiplication, the commutative law states
In terms of the result, the order in which variables
are ANDed makes no difference.
AB = BA
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Figure 4.1
Application of commutative law of addition.
Pp181
Digital Fundamentals, Tenth Edition
Thomas L. Floyd
Copyright ©2009 by Pearson Higher Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Figure 4.2 Application of commutative law of multiplication.
Digital Fundamentals, Tenth Edition
Thomas L. Floyd
Copyright ©2009 by Pearson Higher Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Summary
Associative Laws
The associative laws are also applied to addition and
multiplication. For addition, the associative law states
When ORing more than two variables, the result is
the same regardless of the grouping of the variables.
A + (B +C) = (A + B) + C
For multiplication, the associative law states
When ANDing more than two variables, the result is
the same regardless of the grouping of the variables.
A(BC) = (AB)C
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Figure 4.3 Application of associative law of addition. Open file F04-03 to verify.
Pp181
Digital Fundamentals, Tenth Edition
Thomas L. Floyd
Copyright ©2009 by Pearson Higher Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Figure 4.4 Application of associative law of multiplication. Open file F04-04 to verify.
Digital Fundamentals, Tenth Edition
Thomas L. Floyd
Copyright ©2009 by Pearson Higher Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Summary
Distributive Law
The distributive law is the factoring law. A common
variable can be factored from an expression just as in
ordinary algebra. That is
AB + AC = A(B+ C)
The distributive law can be illustrated with equivalent
circuits: Pp182
B
C
B+ C
A(B+ C)
AB
X
X
A
Floyd, Digital Fundamentals, 10th ed
A
B
A
C
AC
AB + AC
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Figure 4.5 Application of distributive law. Open file F04-05 to verify.
Digital Fundamentals, Tenth Edition
Thomas L. Floyd
Copyright ©2009 by Pearson Higher Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Summary
Rules of Boolean Algebra
Pp182
3. A . 0 = 0
7. A . A = A
8. A . A = 0
=
9. A = A
4. A . 1 = 1
10. A + AB = A
5. A + A = A
11. A + AB = A + B
6. A + A = 1
12. (A + B)(A + C) = A + BC
1. A + 0 = A
2. A + 1 = 1
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved