ENG2410 Digital Design “Sequencing and Control Examples” Fall 2017 S. Areibi School of Engineering University of Guelph

Traffic Light Controller

Example (Traffic Light Controller) Find an ASM chart for a traffic light controller that works as follows: A timing signal T is the input to the controller T defines the yellow light as well as the changes of RED and GREEN lights While T = 0, the green light is on for one signal, the red light is on for other signal While T = 1, the yellow light is on for the signal that was previously green and the signal that was previously red remains red When T becomes 0, the signal that was previously yellow becomes RED and the signal that was previously RED becomes GREEN This pattern continues

Example (Traffic Light Controller) While T = 0, the green light is on for one signal, the red light is on for other signal While T = 1, the yellow light is on for the signal that was previously green and the signal that was previously red remains red When T becomes 0, the signal that was previously yellow becomes RED and the signal that was previously RED becomes GREEN This pattern continues

ASM for Traffic Light Controller GREEN RED YELLOW RED RED GREEN RED YELLOW 1 1 1 1 T T T T Implement using One Flip Flop Per State Implement using Sequence Register and Decoder

Serial Multiplier

Multiplier Example Partial products are: 101 x 0, 101 x 1, and 101 x 1 Example: (101 x 011) Base 2 Note that the partial product summation for n digits, base 2 numbers requires adding up to n digits (with carries) in a column. Note also n x m digit multiply generates up to an m + n digit result (same as decimal). Partial products are: 101 x 0, 101 x 1, and 101 x 1

Example (1 0 1) x (0 1 1) Again Reorganizing example to follow hardware algorithm: Multiplier: Register Q Multiplicand: Register B Scratchpad: Register A 1 x + Clear C || A Multipler0 = 1 => Add B Addition Shift Right (Zero-fill C) Multipler1 = 1 => Add B Shift Right Multipler2 = 0 => No Add, Clear C || A

Hardware ? (Data Path + Control) A Parallel Adder Switches to enter Multiplier/Multiplicand Shift Register Q (Multiplier) Register B (Multiplicand) Counter (to know when to stop) Zero detection circuit (input to control) Shift Register A (scratch pad) Flip Flop to store Carry of Adder Detect when Q0 is zero or one (input to control) A Go signal to start (input to control) Control Output? Load, Load_B, Clear_C, Initialize_A, Shift

Multiplier Datapath: Block Diagram n 2 1 IN n Multiplicand Counter P Register B log n n 2 Zero detect G (Go) C Parallel adder out Z n n Control Q Multiplier o unit C Shift register A Shift register Q 4 n Product Control signals OUT

Multiplier Example: Required Steps The multiplicand (top operand) is loaded into register B (X) The multiplier (bottom operand) is loaded into register Q (X) Register C|| A is initialized to 0 when G becomes 1. The partial products are formed in register C||A||Q. Each multiplier bit, beginning with the LSB, is processed (if bit is 1, use adder to add B to partial product; if bit is 0, do nothing) C||A||Q is shifted right using the shift register Partial product bits fill vacant locations in Q as multiplier is shifted out If overflow during addition, the outgoing carry is recovered from C during the right shift Steps 5 and 6 are repeated until Counter P = 0 as detected by Zero detect. Counter P is initialized in step 4 to n – 1, n = number of bits in multiplier

Multiplier Example: Block Diagram The multiplicand (top operand) is loaded into register B(X) The multiplier (bottom operand) is loaded into register Q(X) C out n 2 1 Counter P Zero detect Control unit G (Go) log Q o Z Parallel adder Multiplicand Register B Shift register A Shift register Q Multiplier Product OUT IN Control signals 4

Multiplier Example: Block Diagram Register C||A is initialized to 0 when G becomes 1. The partial products are formed in register C||A||Q C out n 2 1 Counter P Zero detect Control unit G (Go) log Q o Z Parallel adder Multiplicand Register B Shift register A Shift register Q Multiplier Product OUT IN Control signals 4

Multiplier Example: Block Diagram Each multiplier bit, beginning with the LSB, is processed if bit is 1, use adder to add B to partial product; if bit is 0, do nothing C out n 2 1 Counter P Zero detect Control unit G (Go) log Q o Z Parallel adder Multiplicand Register B Shift register A Shift register Q Multiplier Product OUT IN Control signals 4

Multiplier Example: Block Diagram C||A||Q is shifted right using the shift register Partial product bits fill vacant locations in Q as multiplier is shifted out If overflow during addition, the outgoing carry is recovered from C during the right shift C out n 2 1 Counter P Zero detect Control unit G (Go) log Q o Z Parallel adder Multiplicand Register B Shift register A Shift register Q Multiplier Product OUT IN Control signals 4

Multiplier Example: Block Diagram Steps (5 and 6) are repeated until Counter P = 0 as detected by Zero detect. Counter P is initialized in step 4 to n – 1, n = number of bits in multiplier C out n 2 1 Counter P Zero detect Control unit G (Go) log Q o Z Parallel adder Multiplicand Register B Shift register A Shift register Q Multiplier Product OUT IN Control signals 4

Multiplier Example: ASM Chart (continued) Three states are employed using a Mealy output model: IDLE - state in which: input G is used as the condition for starting the multiplication, and C, A, and P are initialized MUL0 - state in which conditional addition is performed based on the value of Q0. MUL1 - state in which: right shift is performed to capture the partial product and position the next bit of the multiplier in Q0 the terminal count of 0 for down counter P is used to sense completion or continuation of the multiply.

Multiplier Example: ASM Chart 1 G IDLE MUL0 Z MUL1 C ← 0, A ← P ← n – A ← A + B, C out P – C ← 0, C || A || Q ← sr C || A || Q, Q Three states are employed using a Mealy output model: IDLE - state in which: input G is used as the condition for starting the multiplication, and C, A, and P are initialized MUL0 - state in which conditional addition is performed based on the value of Q0. MUL1 - state in which: right shift is performed to capture the partial product and position the next bit of the multiplier in Q0 the terminal count of 0 for down counter P is used to sense completion or continuation of the multiply.

Multiplier Example: Control Unit In implementing a complex control unit, designers usually have to deal with (separate) two distinct aspects The generation of the control signals Sequencing of the operations (what will happen next) We can separate the two aspects by dividing the original ASM specification into two parts: A table that defines the control signals in terms of states and inputs A simplified ASM chart that represents only transitions from state to state

Multiplier Example: Control Signal Table Bloc k Dia g ram Mod u l e Register A : Register B : F lip-F lop C Register Q Cou n ter P :

Multiplier Example: Control Signal Table Bloc k Dia g ram Mod u l e Mi cr oo pe ra ti on Register A : A ← A ← A + B C || A || Q ← sr C || A || Q Register B : B ← IN F lip-F lop C : C ← C ← C ou t Register Q : Q ← IN C || A || Q ← sr C || A || Q Cou n ter P : P ← n – 1 P ← P – 1

Multiplier Example: Control Signal Table Bloc k Dia g ram Contr o l Mod u l e Mi cr oo pe ra ti on Si gn al N a me Register A : A ← I nitia liz e A ← A + B Load C || A || Q ← sr C || A || Q Shift_dec Register B : B ← IN Load_B F lip-F lop C : C ← C lea r _C C ← C Load ou t Register Q : Q ← IN Load_Q C || A || Q ← sr C || A || Q Shift_dec Cou n ter P : P ← n – 1 I nitia liz e P ← P – 1 Shift_dec

Multiplier Example: ASM Chart IDLE MUL0 1 G 1 Q C ← 0, A ← P ← n – 1 A ← A + B, C ← C out MUL1 C ← 0, C || A || Q ← sr C || A || Q, P ← P – 1 1 Z

Multiplier Example: Control Signal Table Bloc k Dia g ram Contr o l Contr o l Mod u l e Mi cr oo pe ra ti on Si gn al N a me Exp r e ssi on Register A : A ← I nitia liz e IDLE · G

Multiplier Example: ASM Chart IDLE MUL0 1 G 1 Q C ← 0, A ← P ← n – 1 A ← A + B, C ← C out MUL1 C ← 0, C || A || Q ← sr C || A || Q, P ← P – 1 1 Z

Multiplier Example: Control Signal Table Bloc k Dia g ram Contr o l Contr o l Mod u l e Mi cr oo pe ra ti on Si gn al N a me Exp r e ssi on Register A : A ← I nitia liz e IDLE · G A ← A + B Load MUL0 · Q0

Multiplier Example: ASM Chart IDLE MUL0 1 G 1 Q C ← 0, A ← P ← n – 1 A ← A + B, C ← C out MUL1 C ← 0, C || A || Q ← sr C || A || Q, P ← P – 1 1 Z

Multiplier Example: Control Signal Table Bloc k Dia g ram Contr o l Contr o l Mod u l e Mi cr oo pe ra ti on Si gn al N a me Exp r e ssi on Register A : A ← I nitia liz e IDLE · G A ← A + B Load MUL0 · Q0 C || A || Q ← sr C || A || Q Shift_dec M UL1

Multiplier Example: Control Signal Table Bloc k Dia g ram Contr o l Contr o l Mod u l e Mi cr oo pe ra ti on Si gn al N a me Exp r e ssi on Register A : A ← I nitia liz e IDLE · G A ← A + B Load MUL0 · Q0 C || A || Q ← sr C || A || Q Shift_dec M UL1 Register B : B ← IN Load_B LO ADB F lip-F lop C : C ← C lea r _C IDLE · G + MUL1 C ← C Load — ou t Register Q : Q ← IN Load_Q LO ADQ C || A || Q ← sr C || A || Q Shift_dec — Cou n ter P : P ← n – 1 I nitia liz e — P ← P – 1 Shift_dec —

Multiplier Example: Control Table (continued) Signals are defined on a register basis LOADQ and LOADB are external signals controlled from the system using the multiplier and will not be considered a part of this design Note that many of the control signals are “reused” for different registers. These control signals are the “outputs” of the control unit With the outputs represented by the table, they can be removed from the ASM giving an ASM that represents only the sequencing (next state) behavior

Multiplier Example: ASM Chart IDLE MUL0 1 G 1 Q C ← 0, A ← P ← n – 1 A ← A + B, C ← C out MUL1 C ← 0, C || A || Q ← sr C || A || Q, P ← P – 1 1 Z

Example - Sequencing Part of ASM 1 IDLE MUL0 01 MUL1 10 00 G Z

Multiplier Control Unit Implementation

Multiplier: One Flip-flop per State Design C IDLE MUL0 MUL1 Initialize Clear _C Load Shift_dec Clock Z Q 4 1 G 2 5 DEMUX A EN START IDLE 00 1 G 01 MUL0 MUL1 10 1 Z

Multiplier: One Flip-flop per State Design School of Engineering

Example: Cont .. Sequence Register and Decoder Design First, define: States: IDLE, MUL0, MUL1 Input Signals: G, Z, Q0 (Q0 affects outputs, not next state) Output Signals: Initialize, LOAD, Shift_Dec, Clear_C State Transition Diagram Output Function. Second, find State Assignments (two bits required) We will use two state bits to encode the three state IDLE, MUL0, and MUL1.

Example: Cont .. Sequence Register and Decoder Design Assuming that state variables M1 and M0 are decoded into states, the next state part of the state table is:

Example: Cont .. Sequence Register and Decoder Design School of Engineering

Example: Cont .. Sequence Register and Decoder Design Finding the equations for M1 and M0 is easier due to the decoded states: M1 = MUL0 M0 = IDLE · G + MUL1 · Z’ Note that since there are five variables, a K-map is harder to use, so we have directly written reduced equations. The output equations using the decoded states: Initialize = IDLE · G Load = MUL0 · Q0 Clear_C = IDLE · G + MUL1 Shift_dec = MUL1

Sequencer and Decoder Design START Initialize G M D Clear_C Z C DECODER IDLE A0 MUL0 1 MUL1 2 Shift_dec A1 3 M 1 D C Load Q

Multiplier Microprogrammed Control

Problems With HardWired Designs Sequencing & micro-operation logic gets complex Difficult to design, prototype, and test Resultant design is inflexible, and difficult to build upon (Pipeline, multiple computation units, etc.) Adding new instructions requires major design and adds complexity quickly

Micro-programmed Control Use sequences of instructions to control complex operations An alternative to a hardwired control unit Called micro-programming, microcode, or firmware

Microprogrammed Control

Micro-Programmed Control A control unit with its binary control values stored as words in memory is called a micro-programmed control. Each word in the control memory contains a microinstruction that specifies one or more micro-operations for the system. A sequence of microinstructions constitutes a microprogram. A micro-program is often fixed at the time of the system design and so is usually stored in ROM. A micro-program can also be written in RAM but has to be loaded initially at system startup. 00101010101100 01110001110000 00000000100000 00011111110000 00001111111111 0010101010101011111111000000 0101010101010100000000000001 11111111111111 microinstruction microprogram Memory

ASM Chart  Microprogrammed Control microinstruction 00101010101100 01110001110000 00000000100000 00011111110000 00001111111111 0010101010101011111111000000 microprogram 0101010101010100000000000001 11111111111111 Memory School of Engineering

Microprogrammed Control Organization Control Memory »A memory is part of a control unit : »Computer Memory (employs a microprogrammed control unit) Main Memory : for storing user program (Machine instruction/data) Control Memory : for storing microprogram (Microinstruction) Data Path ALU + RegFile PC Control Unit Main Memory LDA .. SUB .. IR Sequencer (Next Address Gen) Microinstructions ………………………… ………………………..

Machine Instruction vs Microinstruction Format

A Micro-Programmed Control Unit Organization The microinstruction is stored in the Control Memory (ROM). Control Address Register (CAR) specifies the address of the microinstruction. The Control Data Register (CDR) may hold the instruction currently being executed. The next address generator produces the next address (Sequencer).

A Micro-Programmed Control Unit Organization One of the functions of the control word is to determine the address of the next microinstruction to be executed. This microinstruction may be the next one in sequence Or may be located somewhere else in the control memory Therefore, one or more bits that specify how to determine the address of the next microinstruction must be present in the current microinstruction. The next address may also be a function of status and external control inputs.

Next-address generator (sequencer) Control address register Control memory (ROM) Control data register Control word Next-address information External input Sequencer »Determine the address sequence that is read from control memory »Next address of the next microinstruction can be specified several way depending on the sequencer input. Sequencing Capabilities Required in a Control Storage Incrementing of the control address register (adder/Incrementer) A mapping process from the bits of the machine instruction to an address for control memory

Mapping of Instructions (Mapping Logic)

Control Address Register A Simple Sequencer Implementation “000…000” MUX Control Address Register Incrementer +1 Instruction Register Mapping Logic 010 00101010101100 01110001110000 00000000100000 00011111110000 00001111111111 0010101010101011111111000000 0101010101010100000000000001 11111111111111 001 011 100 011 Control Memory 101 En 011 011 011 … Control Signals (micro-operations)

Multiplier: Original ASM Chart IDLE MUL0 1 G 1 Q C ← 0, A ← P ← n – 1 A ← A + B, C ← C out The structure of the ASM chart has to change to a Moore-type since no conditional output boxes are permitted. This means more states will be required MUL1 C ← 0, C || A || Q ← sr C || A || Q, P ← P – 1 1 Z

Multiplier: Modified ACM Chart The modified ACM chart has two extra states INIT Add Besides being a Moore-type circuit, this ASM has only single decision boxes determining the sequencing between states (simplification). School of Engineering

A Micro-Programmed Control Unit Organization The Control Memory is assumed to be a ROM. The Control Address Register (CAR) specifies the address of the microinstruction. The Control Data Register (CFR), which is optional, may hold the microinstruction currently being executed by the data path and the control unit.

A Micro-Programmed Control Unit Organization One of the functions of the control word is to determine the address of the next microinstruction to be executed. This microinstruction may be the next one in sequence Or may be located somewhere else in the control memory Therefore, one or more bits that specify how to determine the address of the next microinstruction must be present in the current microinstruction. The next address may also be a function of status and external control inputs.

A Micro-Programmed Control Unit Organization The next address generator, in combination with the CAR, is sometimes called a microprogram sequencer. It determines the sequence of instructions that is read from the control memory. The address of the next microinstruction can be specified in several ways: Increment the CAR by one Loading the CAR Possible sources for the load operation include: An address from control memory An externally provided address An initial address to start control unit operation + Load

Multiplier: Control Unit We need to determine three things: The bits in the control word for the microinstructions The size of the ROM and the CAR The structure of the next address generator We can then proceed to design the microsequencer and write the microprogram for binary multiplication. School of Engineering

Multiplier: (1) Control Signals Control Signals for the Microprogrammed Multiplier Control Unit: Initialize Load Clear_C Shift_dec School of Engineering

Multiplier: (1) Control Signals Control Signals for Microprogrammed Multiplier Control Initialize Load Clear_C Shift_dec School of Engineering

Multiplier: (1) Control Signals Microinstruction Control Word Format Data Path datapath 3 2 1 Sequencing SD CC LD IT The remainder of the microinstruction control word is devoted to the sequencing of the control unit. School of Engineering

Multiplier: Sequencing The approach used to define the addresses is a major decision in the sequencer design. There are many possible approaches, but two are most typical. Method #1: Uses two addresses in the microinstruction. Method #2: Uses only a single address. School of Engineering

Multiplier: Sequencing Method #1 (two addresses): Includes the two addresses in the microinstruction controlling the decision. Based on the value of the decision variable, one of the two address values is loaded into the CAR. This method permits the arbitrary assignment of addresses to states and ensures that no states need to be added to provide the desired sequencing. But it requires two addresses in each microinstruction, potentially resulting in a long microinstruction word and wide ROM. School of Engineering

Multiplier: Sequencing Method #2 (one address): Uses a counter with parallel load as the CAR One of the two addresses is obtained from the microinstruction The other is obtained by simply counting up the CAR It requires at most one address per microinstruction word. Assignment of the addresses to the states can be problematic States may have to be added to provide the desired sequencing These states can slow the operation of the system due to the added clock cycles needed to pass through them. School of Engineering

Multiplier: (2) Select Field Microinstruction Control Word Format (Two Addresses) Selection School of Engineering

Multiplier: SEL Field School of Engineering

Multiplier: Control Word Microinstruction Control Word Format Data Path bits Selection bits Next Address #0 Next Address #1 School of Engineering

Microprogrammed Control Unit for Multiplier School of Engineering

Microprogrammed Control Unit for Multiplier School of Engineering

Microprogrammed Control Unit for Multiplier School of Engineering

Microprogrammed Control Unit for Multiplier School of Engineering

Microprogrammed Control Unit for Multiplier 00 School of Engineering

Multiplier The table below gives the register transfer description of the Binary Multiplier Microprogram. Notice that there are 5 states (thus 5 addresses) each activating a specific part of the system. School of Engineering

Multiplier The table below gives the microprogram for the binary multiplier in register transfer notation. There is a microinstruction in the microprogram that corresponds to each of the states in the ASM chart School of Engineering

Microprogrammed Control Given this brief introduction to hardwired and mircro-porgrammed control unit design, we are now prepared to consider more complex control units for programmable digital systems. Our specific focus will start with simple computers, thereby building a basis for studying CPU designs. School of Engineering

VHDL for Binary Multiplier - 1 -- Binary Multiplier with n = 4 library ieee; use ieee.std_logic_1164.all; use ieee.std_logic_unsigned.all; entity binary_multiplier is port(CLK, RESET, G, LOADB, LOADQ: in std_logic; MULT_IN: in std_logic_vector(3 downto 0); MULT_OUT: out std_logic_vector(7 downto 0)); end binary_multiplier;

VHDL for Binary Multiplier - 1 -- Binary Multiplier with n = 4 architecture sequential of binary_multiplier is type state_type is (IDLE, MUL0, MUL1); signal state, next_state: state_type; signal P: std_logic_vector(1 downto 0); signal A,B,Q: std_logic_vector(3 downto 0); signal C,Z: std_logic; begin Z <= P(1) NOR P(0); MULT_OUT <= A &Q state_register: process (CLK, RESET) …….. next_state_func: process (G, Z, state) datapath_func: process (CLK) end sequential;

VHDL for Binary Multiplier - 2 -- state register state_register: process (CLK, RESET) begin if (RESET = '1') then state <= IDLE; elsif (CLK'event and (CLK = '1')) then state <= next_state; end if; end process;

VHDL for Binary Multiplier - 3 -- next state function next_state_function: process (state, G, Z) begin case state is when IDLE => if (G = '1') then next_state <= MUL0; else next_state <= IDLE; end if; when MUL0 => next_state <= MUL1; when MUL1 => if (Z = '1') then end case; end process;

VHDL for Binary Multiplier - 4 -- datapath function Datapath_func: process (CLK) variable CA: std_logic_vector (4 downto 0); begin if (CLK'event and (CLK = '1')) then if (LOADB = '1') then B <= MULT_IN; elsif (LOADQ = '1') then Q <= MULT_IN; end if; case state is when IDLE => if G = '1‘ then C <= ‘0’; A <= "0000"; P <= “11”;

VHDL for Binary Multiplier - 4 -- cont ….datapath function case state is ……. when MUL0 => if Q(0) = ‘1’ then CA := (‘0’ & A) + (‘0’ & B); else CA <= C & A; end if; C <= CA(4); A < CA (3 downto 0); when MUL1 => C =< ‘0’ A <= C & A(3 downto 1); Q <= A(0) & Q(3 downto 1); P = P – “01”; end case; end process

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