Digital Design: Mano, Chapter 8. Control Logic Design
8-1 Introduction
• The logic design of a digital system can be divided into
two distinct parts:
– Data path design: the design of digital circuits that perform the
data processing operations (EX. Arithmetic, logic, shift
operations, etc.
– Control path design: The design of the control circuit that
supervises the operations and determines the sequence in
which they are executed.
• Clocking Disciplines
– The timing of all registers in a synchronous digital system is
controlled by a master clock generator. The clock pulses are
applied to all flip-flops and registers in the system.
– The continuous clock pulses do not change the state of a
register unless the register is enabled by a control signal.
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Digital Design: Mano, Chapter 8. Control Logic Design
• Control and data processor (Fig. 8-1)
– The control logic that generates the signals for sequencing the
operations in the data processor is essentially a sequential
machine. (Mealy machine)
• Next state = F(current state, external inputs, status
conditions)
• Output= G (current state, external inputs, status conditions)
• Control organization
– Two major types of control organization
• Hardwired control: The control logic is implemented with
gates and flip-flops similar to a sequential circuit.
– Advantage: Fast mode of operation
– Disadvantage: Require changes in the wring among various
components if the design has to be modified.
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Digital Design: Mano, Chapter 8. Control Logic Design
• Microprogrammed control: The control information such
as control functions or control words are stored as 1’s and
0’s is a special memory.
– Advantage: Any changes or modifications can be done
merely by changing the contents of the memory.
– Disadvantage: Slow mode of operation
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Digital Design: Mano, Chapter 8. Control Logic Design
8-2 Microprogrammed Control
• The purpose of the control unit in a digital system is to
initiate a series of sequential steps of operations. At any
given time, some operations are to be initiated while
others remain idle.
• The control variables at any given time can be
represented by a string of 1’s and 0’s called a control
word. So the control words can be programmed to
initiate the various components in the data processor.
• A control unit whose binary control variables are
stored in a memory is called a microprogrammed
control unit.
• Each word in control memory is called a
microinstruction.
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Digital Design: Mano, Chapter 8. Control Logic Design
• A sequence of microinstructions constitute the
microprogram.
• The control memory can be a ROM.
• By reading the content of the word in ROM at a given
address specified the microoperations for the data
processor.
• Dynamic microprogramming: A microprogram to be
loaded initially from the computer console or from
magnetic disks.
• Generation configuration of a microprogrammed
control (Fig. 8-2)
– Control address register: Specifies the address of the
microinstruction.
– Control data register: Holds the microinstruction read from
memory.
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Digital Design: Mano, Chapter 8. Control Logic Design
– The location of the next microinstruction is generated by the
sequencer. The location may be the next one in sequence, or it
may be located elsewhere in the control memory. Some bit of
the present microinstruction are used to generate the address
of the next microinstruction.
• Typical functions of a microprogrammed sequencer
– Increment the control address register (CAR) by one. (CAR 
CAR + 1)
– Load into the CAR an address from control memory. (CAR 
CDR)
– Transfer an external address into CAR. (CAR  External
Input)
– Load an initial address into CAR to start the control
operations. (CAR  Initial address)
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Digital Design: Mano, Chapter 8. Control Logic Design
• Control data register
– Data register is sometimes called a pipeline register.
– It allows the microoperations specified by the control word to
be executed simultaneously with the generation of the next
microinstruction, that is, the CAR can be loaded with the
address of next microinstruction while the current
microinstruction is executing.
– This configuration requires a two phase clock, with one phase
applied to the address register (CAR) and the other to the
control data register. (Fig. XX)
• Without control data register
– The system can operate without the control data register by
applying a single phase clock to the address register.
– The CAR can not load a new address while the current
microinstruction is executing. (Fig. XX)
– For our example we will not use the control data register.
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Digital Design: Mano, Chapter 8. Control Logic Design
8-3 Control of Processor Unit
• Microprogrammed control (Fig. 8-3)
• Operation of control unit
– CAR receives a new address at any given clock pulse transition.
– The 26-bit microinstruction is read.
– The control word specifies a microoperation and MUX1 and
MUX2 determine the next operation for CAR.
– The next transition of the clock transfers the result of the
microoperation into destination register, updates the required
status bits, and put a new address into the CAR.
• Encoding of microinstructions
–
–
–
–
Microinstruction format(Table 8-1)
Encoding of ALU operations
Encoding of Shifter operations
Encoding of Select input to MUX2
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Digital Design: Mano, Chapter 8. Control Logic Design
• Examples of microinstructions (Table 8-5)
Address 36: R1  R1  R2, CAR  CAR + 1
Address 40: R3  R3 - 1, CAR  43
Address 52: R4  0, if (S=1) then (CAR  37) else (CAR 
CAR + 1)
Address 56: R5  shl R5, if (C=0) then (CAR  62) else (CAR 
CAR + 1)
Address 59: R2  R6 + R7, CAR  External Address
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Digital Design: Mano, Chapter 8. Control Logic Design
8-4 Microprogram Examples
• Example 1: Perform the following operations:
1. R3  R1 - R2 /* This updates C and Z flags */
2. If R1 < R2 (detected by C=0) then R4  R4 + R1
If R1 > R2 (detected by C=1 and Z=0) then R4  R4 + R2
If R1 = R2 (detected by Z=1) then R4  R4 + 1
3. Output  R4 and branch to external address
X-Y=X-Y+2n-2n=X+(2n-Y-1)+1-2n=X+Y’+1-2n
If X-Y<0 ==> X+Y’+1-2n<0 ==> X+Y’+1<2n ==> No carry
If X-Y >= 0 ==> X+Y’+1 >= 2n ==> with carry
– Register transfer statement (Table 8-6)
– Symbolic microprogram (Table 8-7)
– Binary microprogram (Table 8-8)
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Digital Design: Mano, Chapter 8. Control Logic Design
• Example 2: Counting the number of 1’s
– Problem: Count the number of 1’s stored in register R1 and set
register R2 to that number.
– For example, if R1=00110110 then R2=00000100
– Flowchart (Fig. 8-4)
– Microprogram (Table 8-9)
• The microprogram method is sometimes referred to as
firmware.
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Digital Design: Mano, Chapter 8. Control Logic Design
8.5 Design Example: Binary Multiplier by
Hardwired Control
• The microprogram is too expensive for the design of
small digital systems and not fast enough for high speed
computers.
• The hardwired control is essentially a sequential circuit
whose state at any given time determines the
microoperations to be executed in the data processor
subsystem.
• A multiplier = data processor + control unit
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Digital Design: Mano, Chapter 8. Control Logic Design
• Design of binary multiplier data processor
– Example
23
10111 Multiplicand
19
10011 Multiplier
-------------------------------------------------------10111
10111 Shifted multiplicand
00000
00000
10111
---------------------------------------------------437
110110101 Product
– The product of multiplying two n-bit numbers can have up to
2n bits
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Digital Design: Mano, Chapter 8. Control Logic Design
• Shift-And-Add multiplier
10111
10011
--------00000
10111
--------10111
10111
--------1000101
0000000
-----------1000101
00000
-------------01000101
10111
---------------110110101
Multiplicand
Multiplier
Initial partial product
Shifted multiplicand (SM)
Partial product (PP)
SM
PP
SM
PP
SM
PP
SM
Product
– We will shift the partial product instead of multiplicand.
– If the corresponding bit in the multiplier is 0, no need to add
all 0’s to the partial product.
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Digital Design: Mano, Chapter 8. Control Logic Design
– Register configuration for the multiplier (Fig. 8-5)
• n is the number of bits for the multiplier.
• The counter P is loaded with the value n before
multiplication starts.
– Flowchart for binary multiplier (Fig. 8-6)
– Required registers
• The type of registers needed for the data processor can be
derived from the microoperations listed in the flowchart:
–
–
–
–
–
Register A must be a shift register with parallel load.
Register Q is a shift register.
Register B is a register with parallel load,
Counter P is a binary count-down counter with parallel load.
Flip-flop C should have a synchronous reset.
– Numerical example for binary multiplier (Table 8-10)
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Digital Design: Mano, Chapter 8. Control Logic Design
8-6 Hardwired Control for Multiplier
• The design of a hardwired control is a sequential circuit
design problem.
• The state diagram of the control circuit. (Fig. 8-7)
– Inputs: S, Z, and Q
– Outputs: T0, T1, T2, T3 and L
– The control logic has two inputs Z and S and four outputs, T0,
T1, T2, T3 .
• Hardwired control by sequence register(state memory)
and decoder
– Use a register to sequence the control states and a decoder to
provide an output for each state.
– An n-bit sequence register is essentially a circuit with n flipflops together with the associated gates that effect their state
transitions.
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Digital Design: Mano, Chapter 8. Control Logic Design
– The control state diagram for binary multiplier has four states
and two inputs. We need two flip-flops for the register and a 2to-4 line decoder.
– State table (Transition/excitation and output table) (Table 8-11)
– Excitation equations
DG0 = D0 = D1’ G0’ S + G1 G0’ = T0 S + T2
DG1 = D1 = G1’ G0 +G1 G0’ + G1 G0 Z’ = T1 +T2 +T3 Z
– Logic diagram of the control logic (Fig. 8-9)
• Hardwired control by on flip-flop per state
– Use one flip-flop per state. We need four flip-flops but no
decoder. Only one flip-flop is set to 1 at any particular time; all
others are set to 0.
– One advantage of this method is the simplicity with which it
can be designed. This type of controller can be designed
directly by inspection from the state diagram.
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Digital Design: Mano, Chapter 8. Control Logic Design
– Excitation equations
DT0=T0 S’ + T3 Z
DT1= T0 S
DT2= T1 + T3 Z’
DT3= T2
– Sometimes, the one flip-flop per state controller is implemented
with a register that has common asynchronous input for
resetting all flip-flops initially to 0. Dt0 is modified as follows:
DT0=T0 S’ + T3 Z + T0’ T1’ T2’ T3’
– Logic diagram for one flip-flop per state controller
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Digital Design: Mano, Chapter 8. Control Logic Design
8-7 Example of a Simple Computer
• The user of a computer can control the process of
operations by means of a program.
– A program is a set of instructions that specifies the operations,
operands, and the sequence in which processing is to occur.
– The data processing task may be altered by specifying a new
program with different instructions or by specifying the same
instructions with different data.
– The instruction codes, together with data are stored in memory.
The control reads each instruction from memory and places it
in a control register (instruction register). The control then
interprets the instruction and proceeds to execute it by issuing
a sequence of microoperations.
• The ability to store and execute instructions is the most
important property of the general purpose computer
(i.e., Stored program concept)
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Digital Design: Mano, Chapter 8. Control Logic Design
• Instruction code
– An instruction code is a group of bits that instructs the
computer to perform a specific operation.
– It is usually divided into parts, each having its own particular
interpretation (Opcode + Operands).
– The most basic part of an instruction code is its operation part
(Opcode).
– The operation code of an instruction is a group of bits that
defines an operation, such as add, subtract, shift, ….
• Operation code (Opcode)
– The number of bits required for the operation code of an
instruction is a function of the total number of operations used.
– n bits can specified up to 2n operations.
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Digital Design: Mano, Chapter 8. Control Logic Design
• Operand
– An instruction code must specify not only the operation but
also the registers or memory words where the operands are to
be found.
– Two ways of specifying an operand
• An operand is said to be specified explicitly if the
instruction code contains special bits for its identification.
For example, memory address may be specified explicitly
as an operand.
• An operand is said to be specified implicitly if it is included
as part of the definition of the operation. For example, an
operation that complements a register in the operation part
of the code.
• Instruction code format
– The format of an instruction is usually depicted in a
rectangular box symbolizing the bits of the instruction as they
appear in memory word or in a control register
– Example of an instruction format (Fig. 8-11)
– Numerical example (Fig. 8-12)
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Digital Design: Mano, Chapter 8. Control Logic Design
• Instruction, Operation, and microoperation
– An operation is specified by an instruction stored in computer
memory.
– The operation code bits are interpreted by the control unit as a
sequence of control functions to perform the required
microoperations for the execution of the instruction.
• Block diagram of a simple computer (Fig. 8-13)
– Registers (Table 8-12)
• The accumulator register (AC) is a general purpose
register where the data processing is done.
– Instructions (Table 8-13)
• 8-bit Opcode specifies 256 instructions, but only six
instructions are used here.
• Instruction length is defined by the number of bits used by
Opcode and operands.
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Digital Design: Mano, Chapter 8. Control Logic Design
– A simple program to perform 83-(52+25)
LDI
52
Load 52 into the AC
ADI
25
Add 25 to the AC
CMA
Complement the AC
INA
Increment the AC
ADI
83
Add 83 to the AC
STA
250
Store the contents of the AC in M[250]
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Digital Design: Mano, Chapter 8. Control Logic Design
8-8 Design of a Simple Computer
• Instruction execution cycle
– Instruction fetch phase --> Instruction execution phases -->
Instruction fetch phase ….
– Instruction fetch phase: common to all instructions.
• It fetches the operation code from memory abnd places it
in a control register.
• Timing variables T0 and T1 of the timing decoder are used
as control functions for the fetch phase.
T0: DR  M[PC]
T1: IR  DR, PC  PC + 1
– Instruction execution phase
• For INA instruction
D1T2: AC  AC + 1, TC  0
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Digital Design: Mano, Chapter 8. Control Logic Design
– TC  0 implies that control goes back to timing variable T0
to start the fetch phase and read the operation code of the
next instruction.
• For LDI OPRD instruction
D3T2: DR  M[PC]
D3T3: AC  DR, PC  PC + 1, TC  0
• For LAD ADRS instruction
D5T2: DR  M[PC]
D5T3: AR  DR, PC  PC + 1
D5T4: DR  M[AR]
D5T5: AC  DR, TC  0
– Microoperation sequence for the simple computer (Fig. 8-14)
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Digital Design: Mano, Chapter 8. Control Logic Design
• Control Logic
– The design of the control logic starts from listing the set of
microoperations and control functions.
– The list of microoperations specifies the type of registers and
associated digital functions that must be incorporated into the
data processing part of the system.
– The list of control functions specifies the logic gates required
for the control unit.
– First, scan the register transfer statements and retrieve all
these statements that perform the same microoperation. For
example, from Fig. 8-14, inspect PC  PC + 1, we get
• T1+(D3+D4+D5+D6)T3: PC  PC + 1.
• The associated hardware implementation (Fig. 8-15)
– The list of control variables for microoperations (Table 8-14)
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Digital Design: Mano, Chapter 8. Control Logic Design
– The microoperations of the AC
C4: AC  AC + 1
C5: AC  AC’
C6: AC  DR
C7: AC  AC + DR
– The hardware design of the simple computer (Fig. 8-10)
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Digital Design: Mano, Chapter 8. Control Logic Design
Chapter 8
Control Logic Design
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Digital Design: Mano, Chapter 8. Control Logic Design
Final Project
•
•
•
•
•
Department of Computer Engineering and Science, Yuan-Ze University
Course Name: Logic Design
Date out: June 4
Date due: June 28
Problem Description
–
Modify the simple computer described in Chapter 8 to include the following instructions:
• BZ
branch if Z=1
• BNZ
branch if Z=0
• BC
branch if C=1
• BNC
branch if C=0
• BM
branch if S=1
• BP
branch if S=0
• BV
branch if S=1
• BNV
branch if S=0
• JMPI Internally jump (the target address of the above branch and comes from
DR)
• JMPE Externally jump (the target address comes from outside)
– (all branch and jump instructions have an 8-bit absolute target address)
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Digital Design: Mano, Chapter 8. Control Logic Design
–
–
–
• SUBI
OPRD
Subtract immediate operand
AC<--- AC-OPRD
• AND
OPRD
Logical AND
AC <--- AC AND OPRD
• OR
OPRD
Logical OR
AC<-- AC OR OPRD
• XOR
OPRD
Logical exclusive OR
AC<-- AC XOR OPRD
• XNR
OPRD
Logic exclusive NOR
AC<--- AC XNR OPRD
• NOP
No operation
PC<--- PC + 1
• TEST OPRD
Test (AC is not changed)
AC - OPRD
You have at least to add two input signals as follows:
• START: Start executing a program when START changes from zero to 1. Once a
program starts to execute, START must be set to 0.
• RESET: Reset the computer to initial state when it changes from 0 to 1 and remain
at least 3 consecutive cycles at 1. Once the computer is reset, this signal must be set
to 0.
You must have at least have the following output signals:
• BUSY: It is 1 if a program is executing.
• PCC_8: 8-bits output to show the value of program counter.
• ACC_8: 8-bit output to show the value of accumulator.
• SZVC_4: 4-bit output to show the value of status bits.
You are allowed to add more input and output signals as necessary.
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Digital Design: Mano, Chapter 8. Control Logic Design
•
The following table shows how the execution of an instruction sets the status bit
OPcode
Z
S
C
V
00000001
00000010
00000011
00000100
00000101
00000110
00000111
00001000
00001001
00001010
00001011
00001100
00001101
00001110
00001111
00010000
00010001
00010010
00010011
00010100
00010101
00010110
00010111
INA
CMA
LDI
ADI
SUBI
LDA
STA
BZ
BNZ
BC
BNC
BM
BP
BV
BNV
JMPI
JMPE
AND
OR
XOR
XNR
NOP
TEST
Y
Y
Y
Y
Y
N
N
N
N
N
N
N
N
N
N
N
N
Y
Y
Y
Y
N
Y
Y
Y
Y
Y
Y
N
N
N
N
N
N
N
N
N
N
N
N
Y
Y
Y
Y
N
Y
Y
N
N
Y
Y
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
Y
Y
N
N
Y
Y
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
Y
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Digital Design: Mano, Chapter 8. Control Logic Design
•
•
•
Each Team consists of at most two members
Use VHDL to implement such a computer.
Write a program to sort the following data segment that locates at the memory
address 240. Store the data in ascending order starting at 240. You must make your
program size less than 240 bytes. So you are allowed to use any sorting algorithm
that can achieve this goal.
–
Data segment
Address
Content
240
35
241
67
242
35
243
108
244
7
245
230
246
56
247
78
248
34
249
121
32