�Registers and RTL

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Henry Hexmoor

REGISTER TRANSFER AND MICROOPERATIONS

• Register Transfer Language

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• Register Transfer

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• Bus and Memory Transfers

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• Arithmetic Microoperations

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• Logic Microoperations

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• Shift Microoperations

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• Arithmetic Logic Shift Unit

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Henry Hexmoor

SIMPLE DIGITAL SYSTEMS

• Combinational and sequential circuits can be used to create simple digital systems.

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• These are the low-level building blocks of a digital computer.

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• Simple digital systems are frequently characterized in terms of
• the registers they contain, and
• the operations that they perform.

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• Typically,
• What operations are performed on the data in the registers
• What information is passed between registers

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Henry Hexmoor

MICROOPERATIONS (1)

• The operations on the data in registers are called microoperations.
• The functions built into registers are examples of microoperations
• Shift
• Load
• Clear
• Increment
• …

Register Transfer Language

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MICROOPERATION (2)

An elementary operation performed (during

one clock pulse), on the information stored

in one or more registers

R ← f(R, R)

f: shift, load, clear, increment, add, subtract, complement,

and, or, xor, …

1 clock cycle

Register Transfer Language

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ORGANIZATION OF A DIGITAL SYSTEM

- Set of registers and their functions

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- Microoperations set

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Set of allowable microoperations provided

by the organization of the computer

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- Control signals that initiate the sequence of

microoperations (to perform the functions)

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• Definition of the (internal) organization of a computer

Register Transfer Language

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REGISTER TRANSFER LEVEL

• Viewing a computer, or any digital system, in this way is called the register transfer level

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• This is because we’re focusing on
• The system’s registers
• The data transformations in them, and
• The data transfers between them.

Register Transfer Language

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Henry Hexmoor

REGISTER TRANSFER LANGUAGE

• Rather than specifying a digital system in words, a specific notation is used, register transfer language

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• For any function of the computer, the register transfer language can be used to describe the (sequence of) microoperations

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• Register transfer language
• A symbolic language
• A convenient tool for describing the internal organization of digital computers
• Can also be used to facilitate the design process of digital systems.

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Register Transfer Language

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Henry Hexmoor

DESIGNATION OF REGISTERS

• Registers are designated by capital letters, sometimes followed by numbers (e.g., A, R13, IR)
• Often the names indicate function:
• MAR - memory address register
• PC - program counter
• IR - instruction register

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• Registers and their contents can be viewed and represented in various ways
• A register can be viewed as a single entity:

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​

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• Registers may also be represented showing the bits of data they contain

Register Transfer Language

MAR

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Henry Hexmoor

DESIGNATION OF REGISTERS

Register Transfer Language

R1

Register

Numbering of bits

Showing individual bits

Subfields

PC(H)

PC(L)

15

8

7

0

- a register

- portion of a register

- a bit of a register

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• Common ways of drawing the block diagram of a register

7 6 5 4 3 2 1 0

R2

15

0

• Designation of a register

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Henry Hexmoor

REGISTER TRANSFER

• Copying the contents of one register to another is a register transfer

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• A register transfer is indicated as

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R2 ← R1

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• In this case the contents of register R1 are copied (loaded) into register R2
• A simultaneous transfer of all bits from the source R1 to the destination register R2, during one clock pulse
• Note that this is a non-destructive; i.e. the contents of R1 are not altered by copying (loading) them to R2

Register Transfer

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Henry Hexmoor

REGISTER TRANSFER

• A register transfer such as

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R3 ← R5

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Implies that the digital system has

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• the data lines from the source register (R5) to the destination register (R3)
• Parallel load in the destination register (R3)
• Control lines to perform the action

Register Transfer

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Henry Hexmoor

CONTROL FUNCTIONS

• Often actions need to only occur if a certain condition is true
• This is similar to an “if” statement in a programming language
• In digital systems, this is often done via a control signal, called a control function
• If the signal is 1, the action takes place
• This is represented as:

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P: R2 ← R1

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Which means “if P = 1, then load the contents of register R1 into register R2”, i.e., if (P = 1) then (R2 ← R1)

Register Transfer

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Henry Hexmoor

HARDWARE IMPLEMENTATION OF CONTROLLED TRANSFERS

Implementation of controlled transfer

P: R2 ← R1

Block diagram

Timing diagram

Clock

Register Transfer

Transfer occurs here

R2

R1

Control

Circuit

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​

Load

P

n

Clock

Load

t

t+1

• The same clock controls the circuits that generate the control function

and the destination register

• Registers are assumed to use positive-edge-triggered flip-flops

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SIMULTANEOUS OPERATIONS

• If two or more operations are to occur simultaneously, they are separated with commas

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P: R3 ← R5, MAR ← IR

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• Here, if the control function P = 1, load the contents of R5 into R3, and at the same time (clock), load the contents of register IR into register MAR

Register Transfer

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BASIC SYMBOLS FOR REGISTER TRANSFERS

Capital letters Denotes a register MAR, R2

& numerals

Parentheses () Denotes a part of a register R2(0-7), R2(L)

Arrow ← Denotes transfer of information R2 ← R1

Colon : Denotes termination of control function P:

Comma , Separates two micro-operations A ← B, B ← A

Symbols

Description Examples

Register Transfer

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Henry Hexmoor

CONNECTING REGISTRS

• In a digital system with many registers, it is impractical to have data and control lines to directly allow each register to be loaded with the contents of every possible other registers

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• To completely connect n registers 🡪 n(n-1) lines
• O(n²) cost
• This is not a realistic approach to use in a large digital system

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• Instead, take a different approach
• Have one centralized set of circuits for data transfer – the bus
• Have control circuits to select which register is the source, and which is the destination

Register Transfer

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Henry Hexmoor

BUS AND BUS TRANSFER

Bus is a path(of a group of wires) over which information is transferred, from any of several sources to any of several destinations.

From a register to bus: BUS ← R

Bus and Memory Transfers

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Henry Hexmoor

TRANSFER FROM BUS TO A DESTINATION REGISTER

Three-State Bus Buffers

Bus line with three-state buffers

Reg. R0

Reg. R1

Reg. R2

Reg. R3

Bus lines

2 x 4

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Decoder

Load

D

0

D

1

D

2

D

3

z

w

Select

E (enable)

Output Y=A if C=1

High-impedence if C=0

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Normal input A

Control input C

Select

Enable

0

1

2

3

S0

S1

A0

B0

C0

D0

Bus line for bit 0

Bus and Memory Transfers

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BUS TRANSFER IN RTL

• Depending on whether the bus is to be mentioned explicitly or not, register transfer can be indicated as either

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or

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• In the former case the bus is implicit, but in the latter, it is explicitly indicated

Bus and Memory Transfers

R2 ← R1

BUS ← R1, R2 ← BUS

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MEMORY (RAM)

• Memory (RAM) can be thought as a sequential circuits containing some number of registers
• These registers hold the words of memory
• Each of the r registers is indicated by an address
• These addresses range from 0 to r-1
• Each register (word) can hold n bits of data
• Assume the RAM contains r = 2k words. It needs the following
• n data input lines
• n data output lines
• k address lines
• A Read control line
• A Write control line

Bus and Memory Transfers

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MEMORY TRANSFER

• Collectively, the memory is viewed at the register level as a device, M.
• Since it contains multiple locations, we must specify which address in memory we will be using
• This is done by indexing memory references

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• Memory is usually accessed in computer systems by putting the desired address in a special register, the Memory Address Register (MAR, or AR)
• When memory is accessed, the contents of the MAR get sent to the memory unit’s address lines

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Bus and Memory Transfers

M

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MEMORY READ

• To read a value from a location in memory and load it into a register, the register transfer language notation looks like this:

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• This causes the following to occur
• The contents of the MAR get sent to the memory address lines
• A Read (= 1) gets sent to the memory unit
• The contents of the specified address are put on the memory’s output data lines
• These get sent over the bus to be loaded into register R1

Bus and Memory Transfers

R1 ← M[MAR]

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Henry Hexmoor

MEMORY WRITE

• To write a value from a register to a location in memory looks like this in register transfer language:

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• This causes the following to occur
• The contents of the MAR get sent to the memory address lines
• A Write (= 1) gets sent to the memory unit
• The values in register R1 get sent over the bus to the data input lines of the memory
• The values get loaded into the specified address in the memory

Bus and Memory Transfers

M[MAR] ← R1

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Henry Hexmoor

SUMMARY OF R. TRANSFER MICROOPERATIONS

Bus and Memory Transfers

A ← B Transfer content of reg. B into reg. A

AR ← DR(AD) Transfer content of AD portion of reg. DR into reg. AR

A ← constant Transfer a binary constant into reg. A

ABUS ← R1, Transfer content of R1 into bus A and, at the same time,

R2 ← ABUS transfer content of bus A into R2

AR Address register

DR Data register

M[R] Memory word specified by reg. R

M Equivalent to M[AR]

DR ← M Memory read operation: transfers content of

memory word specified by AR into DR

M ← DR Memory write operation: transfers content of

DR into memory word specified by AR

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Henry Hexmoor

MICROOPERATIONS

• Computer system microoperations are of four types:

- Register transfer microoperations

- Arithmetic microoperations

- Logic microoperations

- Shift microoperations

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Arithmetic Microoperations

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Henry Hexmoor

ARITHMETIC MICROOPERATIONS

• The basic arithmetic microoperations are
• Addition
• Subtraction
• Increment
• Decrement

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• The additional arithmetic microoperations are
• Add with carry
• Subtract with borrow
• Transfer/Load
• etc. …

Summary of Typical Arithmetic Micro-Operations

Arithmetic Microoperations

R3 ← R1 + R2 Contents of R1 plus R2 transferred to R3

R3 ← R1 - R2 Contents of R1 minus R2 transferred to R3

R2 ← R2’ Complement the contents of R2

R2 ← R2’+ 1 2's complement the contents of R2 (negate)

R3 ← R1 + R2’+ 1 subtraction

R1 ← R1 + 1 Increment

R1 ← R1 - 1 Decrement

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Henry Hexmoor

BINARY ADDER / SUBTRACTOR / INCREMENTER

Binary Adder-Subtractor

Binary Incrementer

Binary Adder

Arithmetic Microoperations

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Henry Hexmoor

ARITHMETIC CIRCUIT

S1

S0

0

1

2

3

4x1

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MUX

X0

Y0

C0

C1

D0

FA

S1

S0

0

1

2

3

4x1

​

MUX

X1

Y1

C1

C2

D1

FA

S1

S0

0

1

2

3

4x1

​

MUX

X2

Y2

C2

C3

D2

FA

S1

S0

0

1

2

3

4x1

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MUX

X3

Y3

C3

C4

D3

FA

Cout

A0

B0

A1

B1

A2

B2

A3

B3

0

1

S0

S1

Cin

S1 S0 Cin Y Output Microoperation

0 0 0 B D = A + B Add

0 0 1 B D = A + B + 1 Add with carry

0 1 0 B’ D = A + B’ Subtract with borrow

0 1 1 B’ D = A + B’+ 1 Subtract

1 0 0 0 D = A Transfer A

1 0 1 0 D = A + 1 Increment A

1 1 0 1 D = A - 1 Decrement A

1 1 1 1 D = A Transfer A

Arithmetic Microoperations

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Henry Hexmoor

LOGIC MICROOPERATIONS

• Specify binary operations on the strings of bits in registers
• Logic microoperations are bit-wise operations, i.e., they work on the individual bits of data
• useful for bit manipulations on binary data
• useful for making logical decisions based on the bit value
• There are, in principle, 16 different logic functions that can be defined over two binary input variables

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• However, most systems only implement four of these
• AND (∧), OR (∨), XOR (⊕), Complement/NOT
• The others can be created from combination of these

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Logic Microoperations

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Henry Hexmoor

LIST OF LOGIC MICROOPERATIONS

• List of Logic Microoperations

- 16 different logic operations with 2 binary vars.

- n binary vars → functions

2

2

n

• Truth tables for 16 functions of 2 variables and the

corresponding 16 logic micro-operations

Boolean

Function

Micro-

Operations

Name

x 0 0 1 1

y 0 1 0 1

Logic Microoperations

0 0 0 0 F0 = 0 F ← 0 Clear

0 0 0 1 F1 = xy F ← A ∧ B AND

0 0 1 0 F2 = xy' F ← A ∧ B’

0 0 1 1 F3 = x F ← A Transfer A

0 1 0 0 F4 = x'y F ← A’∧ B

0 1 0 1 F5 = y F ← B Transfer B

0 1 1 0 F6 = x ⊕ y F ← A ⊕ B Exclusive-OR

0 1 1 1 F7 = x + y F ← A ∨ B OR

1 0 0 0 F8 = (x + y)' F ← (A ∨ B)’ NOR

1 0 0 1 F9 = (x ⊕ y)' F ← (A ⊕ B)’ Exclusive-NOR

1 0 1 0 F10 = y' F ← B’ Complement B

1 0 1 1 F11 = x + y' F ← A ∨ B

1 1 0 0 F12 = x' F ← A’ Complement A

1 1 0 1 F13 = x' + y F ← A’∨ B

1 1 1 0 F14 = (xy)' F ← (A ∧ B)’ NAND

1 1 1 1 F15 = 1 F ← all 1's Set to all 1's

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Henry Hexmoor

HARDWARE IMPLEMENTATION OF LOGIC MICROOPERATIONS

0 0 F = A ∧ B AND

0 1 F = A ∨ B OR

1 0 F = A ⊕ B XOR

1 1 F = A’ Complement

S₁ S₀

Output

μ-operation

Function table

Logic Microoperations

B

A

S

S

F

1

0

i

i

i

0

1

2

3

4 X 1

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MUX

Select

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Henry Hexmoor

APPLICATIONS OF LOGIC MICROOPERATIONS

• Logic microoperations can be used to manipulate individual bits or a portions of a word in a register

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• Consider the data in a register A. In another register, B, is bit data that will be used to modify the contents of A

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• Selective-set A ← A + B
• Selective-complement A ← A ⊕ B
• Selective-clear A ← A • B’
• Mask (Delete) A ← A • B
• Clear A ← A ⊕ B
• Insert A ← (A • B) + C
• Compare A ← A ⊕ B
• . . .

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Logic Microoperations

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Henry Hexmoor

SELECTIVE SET

• In a selective set operation, the bit pattern in B is used to set certain bits in A

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1 1 0 0 A_t

1 0 1 0 B

1 1 1 0 A_t+1 (A ← A + B)

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• If a bit in B is set to 1, that same position in A gets set to 1, otherwise that bit in A keeps its previous value

Logic Microoperations

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Henry Hexmoor

SELECTIVE COMPLEMENT

• In a selective complement operation, the bit pattern in B is used to complement certain bits in A

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1 1 0 0 A_t

1 0 1 0 B

0 1 1 0 A_t+1 (A ← A ⊕ B)

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• If a bit in B is set to 1, that same position in A gets complemented from its original value, otherwise it is unchanged

Logic Microoperations

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Henry Hexmoor

SELECTIVE CLEAR

• In a selective clear operation, the bit pattern in B is used to clear certain bits in A

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1 1 0 0 A_t

1 0 1 0 B

0 1 0 0 A_t+1 (A ← A ⋅ B’)

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• If a bit in B is set to 1, that same position in A gets set to 0, otherwise it is unchanged

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Logic Microoperations

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Henry Hexmoor

MASK OPERATION

• In a mask operation, the bit pattern in B is used to clear certain bits in A

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1 1 0 0 A_t

1 0 1 0 B

1 0 0 0 A_t+1 (A ← A ⋅ B)

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• If a bit in B is set to 0, that same position in A gets set to 0, otherwise it is unchanged

Logic Microoperations

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Henry Hexmoor

CLEAR OPERATION

• In a clear operation, if the bits in the same position in A and B are the same, they are cleared in A, otherwise they are set in A

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1 1 0 0 A_t

1 0 1 0 B

0 1 1 0 A_t+1 (A ← A ⊕ B)

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Logic Microoperations

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Henry Hexmoor

INSERT OPERATION

• An insert operation is used to introduce a specific bit pattern into A register, leaving the other bit positions unchanged
• This is done as
• A mask operation to clear the desired bit positions, followed by
• An OR operation to introduce the new bits into the desired positions
• Example
• Suppose you wanted to introduce 1010 into the low order four bits of A: 1101 1000 1011 0001 A (Original) 1101 1000 1011 1010 A (Desired)

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• 1101 1000 1011 0001 A (Original)

1111 1111 1111 0000 Mask

1101 1000 1011 0000 A (Intermediate)

0000 0000 0000 1010 Added bits

1101 1000 1011 1010 A (Desired)

Logic Microoperations

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Henry Hexmoor

LOGICAL SHIFT

• In a logical shift the serial input to the shift is a 0.

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• A right logical shift operation:

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​

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• A left logical shift operation:

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​

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• In a Register Transfer Language, the following notation is used
• shl for a logical shift left
• shr for a logical shift right
• Examples:
• R2 ← shr R2
• R3 ← shl R3

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Shift Microoperations

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Henry Hexmoor

CIRCULAR SHIFT

• In a circular shift the serial input is the bit that is shifted out of the other end of the register.

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• A right circular shift operation:

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​

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• A left circular shift operation:

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​

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• In a RTL, the following notation is used
• cil for a circular shift left
• cir for a circular shift right
• Examples:
• R2 ← cir R2
• R3 ← cil R3

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Shift Microoperations

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Henry Hexmoor

Logical versus Arithmetic Shift

• A logical shift fills the newly created bit position with zero:

• An arithmetic shift fills the newly created bit position with a copy of the number’s sign bit:

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Henry Hexmoor

ARITHMETIC SHIFT

• An left arithmetic shift operation must be checked for the overflow

Shift Microoperations

0

V

Before the shift, if the leftmost two

bits differ, the shift will result in an

overflow

• In a RTL, the following notation is used
• ashl for an arithmetic shift left
• ashr for an arithmetic shift right
• Examples:
• R2 ← ashr R2
• R3 ← ashl R3

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sign

bit

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Henry Hexmoor

HARDWARE IMPLEMENTATION OF SHIFT MICROOPERATIONS

Shift Microoperations

S

0

​

1

H0

MUX

S

0

​

1

H1

MUX

S

0

​

1

H2

MUX

S

0

​

1

H3

MUX

Select

0 for shift right (down)

1 for shift left (up)

Serial

input (I_R)

​

A0

A1

A2

A3

Serial

input (I_L)

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Henry Hexmoor

ARITHMETIC LOGIC SHIFT UNIT

S3 S2 S1 S0 Cin Operation Function

0 0 0 0 0 F = A Transfer A

0 0 0 0 1 F = A + 1 Increment A

0 0 0 1 0 F = A + B Addition

0 0 0 1 1 F = A + B + 1 Add with carry

0 0 1 0 0 F = A + B’ Subtract with borrow

0 0 1 0 1 F = A + B’+ 1 Subtraction

0 0 1 1 0 F = A - 1 Decrement A

0 0 1 1 1 F = A TransferA

0 1 0 0 X F = A ∧ B AND

0 1 0 1 X F = A ∨ B OR

0 1 1 0 X F = A ⊕ B XOR

0 1 1 1 X F = A’ Complement A

1 0 X X X F = shr A Shift right A into F

1 1 X X X F = shl A Shift left A into F

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Shift Microoperations

Arithmetic

​

Circuit

​

Logic

Circuit

​

C

C

4 x 1

​

MUX

Select

0

​

1

​

2

​

3

F

S3

S2

S1

S0

B

A

i

A

D

A

E

shr

shl

i+1

i

i

i

i+1

i-1

i

i

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Henry Hexmoor

HW 7

1. Use D-type flip flops and gates to design a counter with the following repeated binary sequence: 0, 1, 3, 2, 4, 6.

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Henry Hexmoor