Lecture 3: Logic circuit. Combinational circuit and sequential circuit

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1 Lecture 3: Logic circuit Combinational circuit and sequential circuit TRAN THI HONG

2 Content Lecture : Computer organization and performance evaluation metrics Lecture 2: Processor architecture and memory system Lecture 3: Logic circuit: Combinational circuit and sequential circuit Lecture 4: Number system and Its Importance Lecture 5: Hardware design by HDL Lecture 6: Parallel programming Lecture 7: Hardware design by high-level synthesis Lecture 8: Computer system design and its applications 2

3 Lecture Information 3

4 Grading ( 評価 ) Mini-test (4%) Score is based on the number of times that you attend the class and your enthusiastic on doing mini-test. You may get MAX score although your answer is not correct! If you cannot attend the lecture with reasonable reason (ex: attend conference), you can get MAX score if you: Inform about your absent to me via hong@is.naist.jp Study from lecture video and submit mini-test by next time. Home-work: (6%) Score is based on the correction of your home-work Bonus (+%) Your activeness, enthusiastic during the lecture (make question, answer the question, etc.) 4

5 Basic Logic Circuits Basic Logic Gates: Not, And, Or, Xor, Xnor, etc. Combinational Circuits Arithmetic Operator: adder, multiplier, etc. Encoder Multiplexer Comparators Sequential Circuits Memory Elements: Latch, FlipFlop, Register, etc. Sequential Circuits 5

6 brick 6

7 Transistor 7

Overview of Hardware Circuit Design System Block Block

Memory Comb. Circuit: Do specific function. Adder Mul.

Latch Flipflop Digital Circuit Design MUX Comp.

8 Overview of Hardware Circuit Design System Block Block 2 Block N Hardware System Verilog HDL Adder Register Memory Comb. Circuit: Do specific function. Adder Mul. Seq. Circuit: Register, memory, etc. Latch Flipflop Digital Circuit Design MUX Comp. Binary Logic gate: Not, And, Or, etc. Comparator Analog Circuit Design Transistors 8

9 Transistor There are several types of transistor such as: Bipolar junction transistor (BJT) Field-Effect Transistor (FET) Junction gate FET (JFET) Metal-Oxide Semiconductor (MOS) MOSFET 9

10 Basic Logic Gates NOT Gate Logic gates are the element building blocks of a digital circuit. Basic element of logic gate is transistor NOT gate is built from 2 MOS transistors Symbol True-Table Circuit

11 Basic Logic Gates NOR Gate NOR gate is built from 4 transistors: 2 p-type in serial and 2 n-type in parallel Symbol True-Table Circuit

12 Basic Logic Gates OR Gate OR gate is built by adding a NOT gate into NOR gate Symbol NOR Circuit NOT True-Table 2

13 NAND gate is built from 4 transistors: 2 p-type in parallel & 2 n-type in serial Symbol Basic Logic Gates NAND Gate True-Table Circuit 3

14 Basic Logic Gates AND Gate Circuit Symbol True-Table NAND NOT 4

15 Basic Logic Gates XOR Gate Symbol Circuit True-Table 5

16 Basic Logic Gates XNOR Gate Symbol Circuit True-Table 6

17 Minitest-3. How many p-type, n-type CMOS transistors are needed for building: NAND gate OR gate XOR gate XNOR gate 7

18 Minitest-3.: Answer How many p-type, n-type CMOS transistors are needed for building: NAND gate: 2 p-type + 2 n-type CMOS transistors OR gate: 3 p-type + 3 n-type CMOS transistors XOR gate: 4 NOT + 2 NAND + OR = 4 (p + n) + 2 (2p + 2n) + (3p + 3n) = p-type + n-type transistors XNOR gate: p-type + n-type transistors 8

19 Basic Logic Circuits Basic Logic Gates: Not, And, Or, Xor, Xnor, etc. Combinational Circuits Arithmetic Operator: adder, multiplier, etc. Encoder Multiplexer Comparators Sequential Circuits Memory Elements: Latch, FlipFlop, Register, etc. Sequential Circuits 9

20 Combinational Circuits - Arithmetic Circuits - (/4) Basic operator: adder Subtractor is the adder of negative number. Multiplier is the sum of multiple adders Divider is very complex and rarely used in hardware design. Half Adder 2

21 Combinational Circuits - Arithmetic Circuits - (2/4) Full Adder Input Output 2

22 Combinational Circuits - Arithmetic Circuits - (3/4) 4-bit Adder A3 A2 A A + B3 B2 B B C3 C2 C C S3 S2 S S Example: (-3) + (6) (3) A B A B A2 B2 A3 B3 Half Adder C Full C Full C2 Adder Adder Full Adder S S S2 S3 C3 22

23 Combinational Circuits - Arithmetic Circuits - (3/4) Multiplier A2 A A B2 B B A2 A A B + A2 A A B 2 + A2 A A B2 4 Example: (2) (5) + + () A2 B2 P4 A2 B A B2 P3 A2 B A B A B2 A B2 P2 A B A B A B P A B A B P 23

24 Other Combinational Circuits - Decoder - - An n-to-2 n decoder is a multiple output combinational logic circuit with n input and 2 n output signals. - For each possible input condition, one and only one output signal is active. LSB x x n-to2 n Decoder m m Input x x Output m 3 m 2 m m MSB x n- m B (B = 2 n -) Exercise: Design a 2-to-4 decoder 24

25 Other Combinational Circuits - Multiplexer & Demultiplexer - - Multiplexer (or MUX) selects one of many input signals to appear on a single output line - Demultiplexer (or DEMUX) takes a single input signals and routes it to one of several output signals. D D D Y Y D D n D n SEL SEL D D n Y Y MUX DEMUX D D n 25

26 Other Combinational Circuits - Comparator- - A comparator determines the relative magnitude of two binary numbers. - There are many types of comparators such as: A B A B > A Y B < Y 3 A B Y 2 A B = Y 4 Input Output Relationship Y Y 2 Y 3 Y 4 Y 5 A > B A < B A = B Y 5 26

27 Combinational Circuits Combinational circuit: used for calculation Always representing a present state No past state in the circuit A NAND gate out XOR gate out B out = AB A B out = A^B NOT gate A out out = A Out changes when A or B changes; No past, nor next info. 27

28 Combinational Circuits Combinational Circuits Always represent a current state No past state in the circuit Not possible to achieve counter Counter: 2 3 N Q: What will happen on A_plus? A + Comb. Logic A_plus A: A_plus will go w/o stop! No stable state if input is not stable. That s the reason we need sequential circuit. 28

29 Minitest-3.2????????????? = 2 b 29

30 Minitest-3.2: Answer SEL = 2 b = 2 Y = D 2 = 2 b 3

31 Basic Logic Circuits Basic Logic Gates: Not, And, Or, Xor, Xnor, etc. Combinational Circuits Arithmetic Operator: adder, multiplier, etc. Encoder Multiplexer Comparators Sequential Circuits Memory Elements: Latch, FlipFlop, Register, etc. Sequential Circuits 3

32 - Sequential circuit is a circuit that is able to REMEMBER its previous data. - Two main types: Latch Memory Elements FlipFlop Latch Controlled by excitation input signals Two types: - Set latch: force to - Reset latch: force to FlipFlop Controlled by clock signal Many Types: - Master Slave SR FlipFlop - Master Slave D FlipFlop - Master Slave JK FlipFlop - Edge-triggered D FlipFlop - Edge-triggered JK FlipFlop - T FlipFlop Device state is changed immediately Device state is changed after clock cycle 32

33 Memory Elements SR Latch Set Reset Latch Set means output Reset means output e.g. reset status The feedback loop creates stable status S R Q Q S R Q Q Q prev Q prev (stored) (reset) (set) (not used) 33

34 Memory Elements Gate D Latch E D Q Q x Q prev Q prev (stored) (reset) (set) 34

35 D Memory Elements Master/Slave D FlipFlop Accept input Keep (Locked) Q cp cp= D Keep (Locked) Accept input Q cp cp= 35

36 Memory Elements Master/Slave D FlipFlop Register Clock Data in Enable b msb... b b Data out Clock b msb... b b Write_address read_data Memory: is a bank of registers Write_data Write_enable b msb... b b read_address b msb... b b 36

37 Sequential Logic Circuits Definition: Outputs depends on stored information (current state) and current inputs Example: Bank account State = Waiting for new operation (stored value: your current balance) Input = Withdraw or deposit Output = Your new balance Combinational logic and one/or more memory elements are used in sequential logic Mem. Element input Comb. Logic output Sequential Circuit 37

38 Sequential Logic Circuits Mem. Element input Comb. Logic output Sequential Circuit Memory element Provide a lock of current status Combinational logic Calculate new status 38

39 Modeling the Circuit Looking into the memory It stores n-bits bit has two states, as and ; 2 bits have four states, as,,, ; n bits have 2 n states. input Mem. Element Comb. Logic output Sequential Circuit The amount of information to be stored is finite a Finite State Machine (FSM) to describe the 2 n states 39

40 Two Kinds of FSM Models Mealy Machine Outputs are function of the present/current state and the present inputs Major FSM model we use input Mem. Element Comb. Logic Moore Machine Outputs are independent of the inputs i.e. dependent on present state only output Sequential Circuit input Comb. Logic Mem. Element output Sequential Circuit 4

41 Minitest-3.3???? 4

42 Minitest-3.3: Answer???? 42

43 Summary Basic Logic Gates: Not, And, Or, Xor, Xnor, etc. Combinational Circuits Arithmetic Operator: adder, multiplier, etc. Encoder Multiplexer Comparators Sequential Circuits Memory Elements: Latch, FlipFlop, Register, etc. Sequential Circuits 43

Chapter 3 Digital Logic Structures

Chapter 3 Digital Logic Structures Transistor: Building Block of Computers Microprocessors contain millions of transistors Intel Pentium 4 (2): 48 million IBM PowerPC 75FX (22): 38 million IBM/Apple PowerPC