数字电路与逻辑设计英文教学PPT

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数字逻辑电路英文课件 (1)Introduction

With memory and states
The arrangement of the text
Teach in 32 times: Arithmetic and device
Char.1,2,3 7 Combinational circuit
Char.4,6 10 Sequential circuit
Buffer
yx
NOT gate (inverter , INV)
y x
Equation Diagram Truth table
Basic device in digital system
AND gate
y x1 x2
equation
Truth table
diagram
Basic device in digital system
Signals in electric circuit
Real signal : voice, music, moving picture… Analog signal: voltage changed with time Digital signal : sampling values from analog
Digital system
Any inputs and outputs can only be 1 or 0 !
For each output, its state must be determined by all the inputs.
Basic device in digital system
Char.7,8 13 Memory and ADC/DAC 2
Exercise and Exams : 100

数字电路英文版第四单元PPT课件

A(B+C )=AB+AC
第19页/共135页
9.
B
B+C
A
B C
X
A
A
C
AB X
AC
X = A( B + C ) X = A B + A C
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10.
Rules of Boolean Algebra
1. A + 0 = A 7. A * A = A
2. A + 1 = 1 8. A * A = 0
• “Don’t care” A combination of input literals that cannot occur and can be used as a 1 or a 0 on a Karnaugh map.
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• Literal A variable or the complement of a variable. • Product-of-sums (POS) A form of Boolean expression that is
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• Commutative law In addition (ORing) and multiplication (ANDing) of two variables, the order in which the variables are ORed orANDed makes no diffence.
A+B=B+A
A
A+B
B
B
A
第15页/共135页
B+A
5.
Logical Multiplication

数字逻辑设计及应用教学英文课件：Lec18-chap 7

Drive output equation
MAX=Q1 · Q0· EN (3)
11
MAX=…….
Digital Logic Design and Application
Example state machine analysis
Construct state /output table
Q0*= Q0 · EN’+Q0’EN
F (Q, I)
Combinational
Derive output equation from the circuit diagram
Y=G (Q, I)
Combinational
Determine transition equation
Q*=T (F (Q, I))
Sequential
Construct transition/output table
Draw state （transition）diagram
9
Draw timing diagram (optional)
Digital Logic Design and Application
Example state machine
Mealy machine Moore machine
EN EN
F
State Memory
Output logic
G
Next state=F(current state, inputs)
Mealy machine的名字来自这个概念的提出者，在1951年写了A Method for Synthesizing Sequential Circuits的状态机的先驱 G. H. Mealy
D1=Q1 · EN’+Q1’ · Q0 · EN+ Q1 · Q0’ · EN

数字电路系统设计中英文课件教程 07 时序逻辑电路原理-Sequential Logic Design Principles (1)

所有的时序电路对亚稳态都是敏感的
metastable 亚稳态
stable
稳态
stable
稳态
7.2 Latches and Flip-Flops (锁存器与触发器)
—— The Basic Building Blocks of most Sequential Circuits. (大多数时序电路的基本构件)
Clock Frequency: The Reciprocal of the Clock Period
(时钟频率：时钟周期的倒数。）
Clock Tick: The First Edge of Pulse in a clock period or sometimes the period itself.
DIGITAL SYSTEM DESIGN
ESHINE
eshine.li@
Chapter 7 Sequential Logic Design Principles ( 时序逻辑设计原理 )
Latches and Flip-Flops (锁存器和触发器 ) Clocked Synchronous State-Machine Analysis (同步时序分析) Clocked Synchronous State-Machine Design (同步时序设计)
Basic Concepts (基本概念)
Sequential Logic Circuit （时序逻辑电路） Clock Period: The Time between Successive transitions in the same direction.
(时钟周期：两次连续同向转换之间的时间。）

Latches（锁存器）

数字电路系统设计中英文课件教程 04 组合逻辑设计原理-combinational logic design principles

4.1.4 n-Variable Theorems (n变量定理)

Generalized idempotency theorem
( 广义同一律 )

X+X+…+X=X X· · · =X X … X Shannon’s expansion theorems

( 香农展开定理 )
F ( X 1 , X 2 ,, X 1 )
1 1 0 0
1 0 1 0
1 1 1 0
Logic function and its expressions
Voting circuit
C A Switch ABC 1stands for close Truth table B 0 0 1 1 0 0 1 1 C 0 1 0 1 0 1 0 1 Y 0 0 0 0 0 1 1 1
Basic Concepts (基本概念)
Two Types of Logic Circuits(逻辑电路分为两大类): Combinational Logic Circuit（组合逻辑电路）
Outputs depend only on its Current Inputs.
(任何时刻的输出仅取决与当时的输入) 电路特点：无反馈回路、无记忆元件
A 0 Ylight B 0 1 stands for light 0 Y = F (A,B,C ) = A·(B+C) 0 1 Logic A function 1 & 1 B Y ≥1 1 C
Logic diagram
Logic Expression to Truth Table (逻辑表达式真值表)
' X 1 F (1, X 2 ,, X 1 ) X 1 F (0, X 2 ,, X 1 )

数字电路英文版PPT 第二单元

Express the number 47 as a sum of the values of each digit. Solution The digit 4 has a weight of 101, as indicated by its position. The digit 7 has a weight of 1, which is 100, as indicated by its position. 47 = ( 4 X 101) + ( 7 X 100 ) = ( 4 X 10 ) + ( 7 X 1) = 40 + 7 Related Problem Determine the value of each digit in 939.
BCD : Binary coded decimal; a digital
code in which each of the decimal digits, 0 through 9, is represented by group of four bits. Byte : A group of eight bits. Carry : The digit generated when the sum of two binary digits exceeds 1.
Weight [ 权 ] Carry [ 进位 Remainder [ 余数 ] Quotient [ 商 Integer [ 整数 ] Fraction [ 小数 1’Complement [ 反码 ] 2’Complement [ 补码 ] Format [ 格式 ] Precision [ 精度 Mantissa [ 尾数 ]

Largest decimal number = 2n – 1 if n = 5 , 25 – 1 = 32 – 1 = 31 if n = 6 , 26 – 1 = 64 – 1 = 63

数字电路系统设计中英文课件教程 01 数字系统简介-introduction to Digital System Design

Combinational Circuits（组合电路） Sequential Circuits（时序电路）
Integrated Circuits
• Classified by size
SSI MSI LSI VLSI
(small-scale integration) (medium) (large) (very large)
Analyse, Design, Test
• Analyse logic relationship between input & output Boolean algebra
Truth table, Functional diagram, Boolean expression, Waveform
The most basic digital devices (AND Gate, OR Gate, and NOT Gate or Inverter)
最基本的数字器件（与、或、非门或反相器）
Flip-flops（触发器）： A device that stores either 0 or 1
一种能存储 0 或 1 的器件
• Design circuit • Test
Computer-aided design(CAD)
Computer-aided engineering (CAE)
1. Scheme & HDL
Computer-aided design(CAD)
Computer-aided engineering (CAE)
结果再现性（稳定可靠、精度更高）
– Ease of design, Flexibility, and Functionality

数字逻辑电路英文课件Minimization logic circuit Karnaugh map

More examples of minimal sum
Some concept
Imply :a rectangular set of 1s; Prime implicant: a maxim imply; Complete sum: sum of all the prime implicant; Distinguished 1-cell: only in one prime implicant; Essential prime implicant :with distinguished 1cell in it.
Minimal product Get a minimal sum-product equation
Step 1 get minimal sum for inverse function Step 2 use DeMorgen’s theorem to get minimal product of the function
Can be minimized by karnaugh map
Байду номын сангаас
Minimal sum Get a minimal product-sum equation
Step 1 :Make rectangular sets of 1s Cover all the 1s in the Kanaugh maps; The cell-numbers in any sets must be 2i ; The number of sets must be minimal ! Each set must be maximal ! (Any 1s can be reused in the process !)
examples:

数字电路与逻辑设计英文教学PPT课件

blows selected internal fuse links. After blowing the fuses,
the array represents the Boolean logic expression for the
desired circuit.
A
A
B
B
What function is
PALs have a one time
A
A
B
B
programmable (OTP)
array, in which fuses are
permanently blown,
X
creating the product
terms in an AND array.
Simplified AND-OR array
Summary
Programmable Logic
Programmable Logic Devices (PLDs) are ICs with a large number of gates and flip flops that can be configured with basic software to perform a specific logic function or perform the logic for a complex circuit. Major types of PLDs are:
SPLD: (Simple PLDs) are the earliest type of array logic used for fixed functions and smaller circuits with a limited number of gates. (The PAL and GAL are both SPLDs).

数字逻辑电路英文课件 (20)Sequential logic design example

States analyze examples: combination lock
Step 3: finish the state diagram with incorrect input sequence ;
States analyze examples: combination lock
Step 4: from the state diagram to the
Sequential logic design example
Design a generator for the periodic sequence (10110） as the clk triggered.
The state diagram
The state/output table
A generator for the periodic sequence
The output equation
CO Q2'Q1'Q0'a'Q2Q1Q0 a a combination lock:
The UNLOCK should be 1 if and only if X is 0 and the sequence of inputs received on X at the preceding seven clock ticks was 0110111. The HINT output should be 1 if and only if the current value of X is the correct one to move the machine closer to being in the “unlocked” state (with UNLK = 1) .

数字电路与逻辑设计课件-Verilog语言总结

specparam、event
数字电路与逻辑设计2016
7
Verilog HDL语言基础
Verilog HDL数据类型和变量
例： wire a,b; wire [7:0] c; reg [7:0] buffer;
数字电路与逻辑设计2016
8
Verilog HDL语言基础
基础运算符
与（&&）、或（||）、非（!）按位与（&）、按位或（|）、按位取反（~）异或（^）、同或（^~ 或者 ~^）移位运算符（<<、>>）关系运算符（>、<、>=、<=）等式运算符（==、!=、===、!==）拼接运算符（{}）
为10进制
例 10
'o7 1'b1 8'Hc5 6'hF0 6'hF 6'hZ
未定长 10进制未定长 8进制 1 bit 2进制 8 bits 16进制 6 bits 16进制 6 bits 16进制 6 bits 16进制
说明 0...01010 (32-bits)
0...00111 (32-bits) 1 11000101 110000 (高位被截断) 001111 (高位由0填充) ZZZZZZ (高位由Z填充)
Verilog HDL数据类型和变量
连线型（Net Type）
wire、tri
wor、wand、trior、triand、tri0、tri1、supply0、supply1、 trireg
寄存器型（Reg Type）
在时序部分出现
reg
integer、time、real
其他
parameter

数字逻辑电路英文课件 (26)Synchronous design methodology

tr tclk tsetup
How to make the tr larger ?
Choose a faster flip-flop : f 25MHz a 2MHz tclk 40
74LS74 (97) :
1.35 T0 4.8103 tsetup 20 MTBF 2.83105 s
may be decided by an exponential formula:
MTBFtr
exptr
T0 f
/
a
MTBF Example: given condition as follows (74LS74)
T0 0.4 1.5 f 107 a 105
MTBFBiblioteka 80ns exp80 /1.5
Tclk > Tsetup + Thold
The time margins in design
Hold time margin : tcq tcomb thold Setup time margin: tclk tcq tcomb tsetup
Clock skew
Hold time margin : tcq tcomb thold tskew Setup time margin: tclk tcq tcomb tsetup tskew
0.4 107 105
3.631011 s
MTBF 40ns exp40 /1.5 9.53101s
0.4 107 105
How to make the tr larger ?
tr tclk tcomb tsetup Use cascade D flip-flops to minimize tcomb
Synchronous design methodology

数字逻辑电路英文课件 (19)State-machine design

A mode 5 counter design
state diagram
state/output table
A mode 5 counter design
State assignment
binary code Gray code one-hot code
S0 0 0 0 S1 0 0 1 S2 0 1 0 S3 0 1 1 S4 1 0 0
The excitation tables for JK flip-flop
J 2 Q1Q0
J1 Q0
J 0 Q2hesis with J-K flip-flop
minimal cost
CO Q2
J 2 Q1Q0 K 2 1
J1 Q0
K1 Q0
Minimize the logic equations
one-hot code CO Q4 D4 Q3 D3 Q2
D2 Q1 D1 Q0 D0 Q4
Ring counter
The excitation tables for JK flip-flop
Characteristic equation Q* J Q'K'Q Divide each transition table into two excitation tables
Construct the transition/output table
binary code
one-hot code
Gray code
Minimize the logic equations
Excitation table for binary code
minimal cost
minimal risk

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of Sum) form for the output (5
points)
01 1 1 0 1
3. Write the minimum SOP form. Draw the circuit. (10 points)
11 0 0 x 1
4. Write the minimum POS form. Draw the circuit (10 points)
The second half-adder has inputs of 1 and 1; therefore the Sum = 0 and the Carry out = 1.
The OR gate has inputs of 1 and 0, therefore the final carry out = 1.
Cout S
00 01 01 10 01 10 10 11
S AS B Cin Cout
Symbol
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
A full-adder can be constructed from two half adders as shown:
A AS S
AS S
Sum
B
B Cout
Cin
B Cout
Cout
Inputs
A B Cin
00 0 00 1 01 0 01 1 100 101 110 111
Outputs
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Parallel Adders
Full adders are combined into parallel adders that can add binary numbers with multiple bits. A 4-bit adder is shown.
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Full-Adder Notice that the result from the previous example can be read directly on the truth table for a full adder.
Summaryຫໍສະໝຸດ Full-Adder1
S A
S
1
AS S 0
Sum
0
B Cout 0
B Cout 1
For the given inputs, determine 1 the intermediate and final outputs
Cout
1
of the full adder.
The first half-adder has inputs of 1 and 0; therefore the Sum =1 and the Carry out = 0.
Digital Fundamentals
Tenth Edition
Floyd
Chapter 6
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education©, U2p0p0e8rPSeaadrdsolenREidvuecr,aNtioJn07458. All Rights Reserved
Quiz 2 (20 minutes)
Refer to Karnaugh map :
1. Write the standard SOP (Sum of
CD
Product) form for the output (5 AB
00 01 11 10
points)
2. Write the standard POS (product 00 1 0 1 1
00 01 01 10
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Full-Adder
By contrast, a full adder has three binary inputs (A, B, and Carry in) and two binary outputs (Carry out and Sum). The truth table summarizes the operation.
10 1 0 1 1
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Half-Adder
Basic rules of binary addition are performed by a half adder, which has two binary inputs (A and B) and two binary outputs (Carry out and Sum).
Inputs
A B Cin
00 0 00 1 01 0 01 1 100 101 110 111
Outputs
Cout S
00 01 01 10 01 10 10 11
1
S A
S
1
AS S 0
0
B Cout 0
B Cout 1
1
Sum
Cout 1
Floyd, Digital Fundamentals, 10th ed
The inputs and outputs can be summarized on a truth table.
The logic symbol and equivalent circuit are:
AS S
S
A
B Cout
B
Cout
Inputs Outputs
AB
00 01 10 11
Cout S