Sequential and combinational alu

Introduction to ALU
Introduction to CombinationalCircuits
Design Procedure of Combinational
Circuits
Analysis Procedure of Combinational
Circuits
Introduction to SequentialCircuits
Types of SequentialCircuits

 ALU stands for: Arithmetic Logic Unit
 ALU is a digital circuit that performs
Arithmetic (Add, Sub, . . .) and Logical (AND,
OR, NOT) operations.
 JohnVon Neumann proposed the ALU in 1945
when he was working on EDVAC.

 AnALU is the fundamental unit of any computing
system.
 Understanding how an ALU is designed and how it
works is essential to building any advanced logic
circuits.
 Using this knowledge and experience, we can move
on to designing more complex integrated circuits.
 TheALU is the “heart” of a processor—you could say
that everything else in the CPU is there to support the
ALU.

Typical Schematic Symbol of an ALU
A and B: the inputs to the ALU
(aka operands)
R: Output or Result
F: Code or Instruction from the
Control Unit (aka as op-code)
D: Output status; it indicates cases
such as:
•carry-in
•carry-out,
•overflow,
•division-by-zero
•And . . .

 COMBINATIONALCIRCUITS
 SEQUENTIALCIRCUITS

 Combinational Circuits are made of logic
gates.
 Doesn’t contain memory element , that’s
why they cant store any information.
 Value of present output is determined by
present input.
 Examples of combinational circuits are half
adders, full adders, sub tractors etc.

 Multiplexer
 Demultiplexer
 Encoder
 Decoder
 Half Adder
 Full Adder

 Multiplexer-
 A multiplexer is a combinational circuit where binary
information from one of many input lines is selected
and directs it to a single output line.
 Demultiplexer-
 Demultiplexing is the reverse process of multiplexing;
i.e., a demultiplexer is a combinational circuit that
receives information on a single line and transmits
this information on one of 2n possible output lines.

 Encoder-
 An encoder is a combinational circuit that
produces the reverse function from that of a
decoder.
 Decoder-
 A decoder is a combinational logic circuit that
receives coded information on n input lines and
feeds them to maximum of 2n unique output lines
after conversion.

 Half-Adder :
 A half-adder is a combinational circuit that performs
the addition of two bits.
 Full Adder :
 This type of adder is a little more difficult to
implement than a half-adder.
 The main difference between a half-adder and a full-
adder is that the full-adder has three inputs and two
outputs.

This procedure involves the following steps:
 The problem is stated.
 The number of available input variables and output variables is
determined.
 The input and output variables are assigned letter symbols.
 Truth table is drawn
 Boolean function for output is obtained.
 The logic diagram is drawn.

 TO DETERMINETHE OUTPUT FUNCTIONS AS
ALGEBRAIC EXPRESSIONS.
 It is the reverse process of design procedure.
 Logic diagram of the circuit is given.
 Obtain the truth table from the diagram.
 Obtain Boolean function from theTruthTable
for output.

 Made up of combinational circuits and memory
elements.
 These memory elements are devices capable of
storing ONE-BIT information.
 Output depends on input and previous state.
 Examples of sequential circuits are flip flops,
counters, shift registers

 Flip-Flops
 JK Flip-Flop
 RS Flip-Flop
 PR Flip-Flop
 D Flip-Flop
 Registers
 Counters

 Flip-Flops are the basic building blocks of sequential
circuits.
 A flip-flop is a binary cell which can store a bit of
information.
 A basic function of flip-flop is storage, which means
memory. A flip-flop (FF) is capable of storing 1 (one) bit of
binary data.
 It has two stable states either ’1’ or ‘0’. A flip-flop
maintains any one of the two stable states which can be
treated as zero or one depending on presence and
absence of output signals.

 A circuit with flip-flops is considered a sequential circuit even in
the absence of combinational logic.
 Circuits that include flip-flops are usually classified by the function
they perform.
 Two such circuits are registers and counters:
 Registers-
 It is a group of flip-flops.
 Its basic function is to hold information within a digital system so as to
make it available to the logic units during the computing process.
 Counters-
 It is essentially a register that goes through a predetermined sequence
of states.

Sequential circuits are of two types:
 SYNCHRONOUS SEQUENTIAL CIRCUITS
 ASYNCHRONOUS SEQUENTIAL CIRCUITS

 In synchronous sequential circuits, the state of
the device changes only at discrete times in
response to a clock Pulse.
 In a synchronous circuit, an electronic
oscillator called a clock generates a sequence of
repetitive pulses called the clock signal which is
distributed to all the memory elements in the
circuit.

 Asynchronous circuit is not synchronized by a
clock signal; the outputs of the circuit change
directly in response to changes in Inputs.
 The advantage of asynchronous logic is that it
can be faster than synchronous logic, because
the circuit doesn't have to wait for a clock signal
to process inputs.
 The speed of the device is potentially limited
only by the propagation delays of the logic
gates used.

This process involves the following steps :
 Make a state table based on the problem statement.The table should
show the present states, inputs, next states and outputs. (It may be
easier to find a state diagram first, and then convert that to a table)
 Assign binary codes to the states in the state table, if you haven’t already. If
you have n states, your binary codes will have at least
log2 n digits, and your circuit will have at least log2 n flip-flops
 For each flip-flop and each row of your state table, find the flip-flop input
values that are needed to generate the next state from the present state.
You can use flip-flop excitation tables here.
 Find simplified equations for the flip-flop inputs and the outputs.
 Build the circuit!

 The Boolean function for outputs are:
T1=A+B+C
T2=ABC
T3=F2’T1
 Outputs functions for gates are :
F1=T3+T2
F2=AB+AC+BC

 F2=AB+AC+BC
 F1=A’BC’+A’B’C+AB’C’+ABC

 Weblinks :
 http://www.google.com
 http://www.wikipedia.com
 http://www.slideshare.net
 http://www.kkhsou.in
 Books :
 ComputerOrganization and Architecture (8th Edition)-
William Stallings
 Schaum’s Outline ofTheory & Problems of Computer
Architecture- McGraw Hill

Sequential and combinational alu

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Sequential and combinational alu