Chapter 3 Digital Logic Structures

What is semiconductor (반도체)? 도체 (conductor), 부도체 (insulator), 반도체 (semiconductor) Dr. Walter Brattain on Semiconductor Physics https://www.youtube.com/watch?v=EWZsnLvL400

Semiconductor: Silicon Conceptually…. In Reality….

n-type and p-type Semiconductor n-type semiconductor p-type semiconductor

Source: http://www.electronics-tutorials.ws/diode/diode_2.html P-N Junction Diode depletion region Reverse biased Forward biased Source: http://www.electronics-tutorials.ws/diode/diode_2.html http://www.electronics-tutorials.ws/diode/diode_3.html

BJT(Bipolar Junction Transistor) N-P-N Transistor Emitter (E) Base (B) Collector (C) Common emitter configuration Source: https://qph.ec.quoracdn.net/main-qimg-9b58be1f7188ec19810ca02284ee111c

MOS(Metal-Oxide-Silicon) Transistor: n-type n-type transistor as a switch G=0 G=1

Keep it simple BJT MOS Transistor "Perfection is achieved not when there is nothing more to add, but when there is nothing left to take away"      Antoine de Saint-Exupery BJT MOS Transistor Source http://gumho.img3.kr/radio/52sanyosf-78green/sanyosf-78green-3.jpg http://techreport.com/r.x/core-i7/die-callout.jpg

Simplicity Wins

노벨상도 실수를 한다? 1956년 Nobel Prize in Physics William Bradford Shockley, John Bardeen, and Walter Houser Brattain “for their researches on semiconductors and their discovery of the transistor effect” The field-effect transistor (a predecessor of the MOS transistor) was first patented by Julius Edgar Lilienfeld in 1926

n-type MOS Transistor Gate = 1 Gate = 0 when Gate has positive voltage, short circuit between #1 and #2 (switch closed) when Gate has zero voltage, open circuit between #1 and #2 (switch open) Gate = 1 Gate = 0

p-type MOS Transistor p-type is complementary to n-type Gate = 1 when Gate has positive voltage, open circuit between #1 and #2 (switch open) when Gate has zero voltage, short circuit between #1 and #2 (switch closed) Gate = 1 Gate = 0

Primitive (CMOS) Gate: Inverter (NOT) gate Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. In Out 1 1 In Out +V

CMOS Circuit Complementary MOS Uses both n-type and p-type MOS transistors p-type Attached to + voltage Pulls output voltage UP when output is one n-type Attached to GND Pulls output voltage DOWN when output is zero For all inputs, make sure that output is either connected to GND or to +, but not both! (+V) (GND) Source: https://3.bp.blogspot.com/-Yfr5bIYOGJc/VtMoo9Y8BoI/AAAAAAAAAF8/POvHrRll9RM/s1600/CMOSBD.png

Primitive Gate: NAND gate B Out 1 1 1 1

Primitive Gate: AND gate Composition!! A B Out 1 1 1 1

Primitive Gate: NOR gate Duality!! C D Out 1 1 1 1

Primitive Gate: OR gate Analogy!! C D Out 1 1 1 1

Basic Logic Gates

Source http://www.learnabout-electronics.org/Digital/dig23.php DeMorgan's Law Consider the following gate: A+B = A B = A+B Alternatively, = A+B Thus A+B = A B 1 Source http://www.learnabout-electronics.org/Digital/dig23.php

Source http://www.learnabout-electronics.org/Digital/dig23.php Additional Laws Operations with 0 and 1 A ∙ 1 = A A + 0 = A A ∙ 0 = 0 A + 1 = 1 Idempotent theorem A ∙ A = A A + A = A Source http://www.learnabout-electronics.org/Digital/dig23.php

More than 2 Inputs? AND/OR can take any number of inputs. AND = 1 if all inputs are 1. OR = 1 if any input is 1. Similar for NAND/NOR. Can implement with multiple two-input gates, or with single CMOS circuit.

Building Functions from Logic Gates Combinational Logic Circuit output depends only on the current inputs stateless Sequential Logic Circuit output depends on the sequence of inputs (past and present) stores information (state) from past inputs We'll first look at some useful combinational circuits, then show how to use sequential circuits to store information.

Decoder 2-bit decoder n inputs, 2n outputs exactly one output is 1 for each possible input pattern 2-bit decoder

Multiplexer (MUX) 4-to-1 MUX n-bit selector and 2n inputs, one output output equals one of the inputs, depending on selector 4-to-1 MUX

Full Adder Add two bits and carry-in, produce one-bit sum and carry-out. A B Cin S Cout 1

Four-bit Adder

Logical Completeness Can implement ANY truth table with AND, OR, NOT. 1 1. AND combinations that yield a "1" in the truth table. 2. OR the results of the AND gates.

Combinational vs. Sequential Combinational Circuit always gives the same output for a given set of inputs ex: adder always generates the same sum and carry, regardless of previous inputs Sequential Circuit stores information output depends on stored information (state) plus input so the same input might produce different outputs, depending on the stored information example: ticket counter advances when you push the button output depends on previous state useful for building “memory” elements and “state machines”

R-S Latch: Simple Storage Element To reset, R = 0, S = 1 (“Active Low” logic – “0” means active) R is used to “reset” or “clear” the element S is used to “set” the element R changes to zero 1 Output changes to zero. 1 ? ? 1 ? ?

R-S Latch: Simple Storage Element To set, R = 1, S = 0 (Again, “Active Low” logic) R is used to “reset” or “clear” the element S is used to “set” the element S changes to zero Output changes to one. ? ? 1 ? ? 1 1 1

R-S Latch: Simple Storage Element If R = S = 1, “quiescent” state -- holds its previous value R is used to “reset” or “clear” the element S is used to “set” the element 1 1 1 1 1 1 1 1 1

R-S Latch (active low) Summary set value to 0 S = 0, R=1 set value to 1 R = S = 1 hold the current value in latch R = S = 0 both outputs equal one but when R and S return to R = S = 1, the output oscillates between 0 and 1 and the final state is determined by electrical properties of gates Don’t do it!

Gated D-Latch Two inputs: D (data) and WE (write enable) when WE = 1, latch is set to value of D S = NOT(D), R = D when WE = 0, latch holds the previous value S = R = 1

Register A register stores a multi-bit value. We use a collection of D-latches, all controlled by a common WE. When WE=1, n-bit value D is written to register.

Representing Multi-bit Values Number bits from right (0) to left (n-1) just a convention -- could be left to right, but must be consistent Use brackets to denote range: D[l:r] denotes bit l to bit r, from left to right May also see A<14:9>, especially in hardware block diagrams. 15 A = 0101001101010101 A[14:9] = 101001 A[2:0] = 101

Memory Now that we know how to store bits, we can build a memory – a logical k × m array of stored bits. • Address Space: number of locations (usually a power of 2) k = 2n locations Addressability: number of bits per location (e.g., byte-addressable) m bits

22 x 3 Memory word WE word select input bits address write enable decoder output bits

Also, non-volatile memories: ROM, PROM, flash, … More Memory Details This is a not the way actual memory is implemented. fewer transistors, much more dense, relies on electrical properties But the logical structure is very similar. address decoder for word select line word write enable Two basic kinds of RAM (Random Access Memory) Static RAM (SRAM) fast, maintains data as long as power applied Dynamic RAM (DRAM) slower but denser, bit storage decays – must be periodically refreshed Also, non-volatile memories: ROM, PROM, flash, …

State Machine Another type of sequential circuit Inputs Outputs Combines combinational logic with storage “Remembers” state, and changes output (and state) based on inputs and current state State Machine Inputs Outputs Combinational Logic Circuit Storage Elements

Combinational vs. Sequential Two types of locks 30 15 5 10 20 25 4 1 8 Combinational Success depends only on the values, not the order in which they are set. Sequential Success depends on the sequence of values (e.g, R-13, L-22, R-3).

State The state of a system is a snapshot of all the relevant elements of the system at the moment the snapshot is taken. Examples: The state of a basketball game can be represented by the scoreboard. Number of points, time remaining, possession, etc. The state of a go game (바둑) can be represented by the placement of ’s and ’s on the board, whose turn, and the number of ’s and ’s taken to the opponents.

State of Sequential Lock Our lock example has four different states, labelled A-D: A: The lock is not open, and no relevant operations have been performed. B: The lock is not open, and the user has completed the R-13 operation. C: The lock is not open, and the user has completed R-13, followed by L-22. D: The lock is open.

State Diagram Shows states and actions that cause a transition between states.

Finite State Machine A description of a system with the following components: A finite number of states A finite number of external inputs A finite number of external outputs An explicit specification of all state transitions An explicit specification of what determines each external output value

The Clock Frequently, a clock circuit triggers transition from one state to the next. At the beginning of each clock cycle, state machine makes a transition, based on the current state and the external inputs. “1” “0” One Cycle time

Implementing a Finite State Machine Combinational logic Determine outputs and next state. Sequential logic: Storage elements Maintain state representation. State Machine Inputs Outputs Combinational Logic Circuit Storage Elements Clock

Storage: Master-Slave Flipflop A pair of gated D-latches, to isolate next state from current state. During 1st phase (clock=1), previously-computed state becomes current state and is sent to the logic circuit. During 2nd phase (clock=0), next state, computed by logic circuit, is stored in Latch A.

Storage Each master-slave flipflop stores one state bit. The number of storage elements (flipflops) needed is determined by log (number of states) Examples: Sequential lock Four states – two bits Basketball scoreboard 7 bits for each score, 5 bits for minutes, 6 bits for seconds, 1 bit for possession arrow, 1 bit for half, … 2

DANGER MOVE RIGHT Complete Example A blinking traffic sign No lights on 1 & 2 on 1, 2, 3, & 4 on 1, 2, 3, 4, & 5 on (repeat as long as switch is turned on) 3 4 1 5 2 DANGER MOVE RIGHT

Traffic Sign State Diagram Switch on Switch off State bit S1 State bit S0 Outputs Transition on each clock cycle.

Traffic Sign Truth Tables Outputs (depend only on state: S1S0) Next State: S1’S0’ (depend on state and input) Switch Lights 1 and 2 Lights 3 and 4 In S1 S0 S1’ S0’ X 1 Light 5 S1 S0 Z Y X 1 Whenever In=0, next state is 00.

Master-slave flipflop Traffic Sign Logic Master-slave flipflop

LC-3 Data Path Combinational Logic Storage State Machine GateMDR

(추가 component) – Tri-state buffer IN OUT enable

(추가 component) – ALU (Arithmetic Logic Unit) 16 16 FUNC = 00 OUT = A + B FUNC = 01 OUT = A • B FUNC = 10 OUT = ¬ A FUNC = 11 OUT = A B A 2 ALU FUNC 16 OUT

(추가 component) – Register File Holds values of registers R0~R7 Can read two registers and write one register in one cycle Reading Like combinational logic Output data based on register # (i.e., SR1 and SR2) Writing Like register Update synchronized by clock

(추가 component) – Register File Source: https://i.stack.imgur.com/FZBHp.png

꼭 기억해야 할 것 Levels of abstraction MOS Transistor / CMOS circuits Importance of simplicity CMOS gates Inverter NAND, AND NOR, OR Circuits Combinational circuits Sequential circuits Finite State Machine