L6-CombSequAdders

8/6/2019 L6-CombSequAdders

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Combinational and Sequential circuits

Any circuit can be configured under either combinational or sequential circuit, i.e. there are 2 types of logic circuits.

Digital

electronics

Combinational

circuitSequential circuit



n input

Variables

Combinational

Circuit m output

Variables

� Combinational circuit is one whose O/P at a specified time is

function of the inputs at that time.� O/P depends purely upon PRESENT input.

� No memory element required to store past inputs.

� Its operations can be completely described by a truth table/

Boolean expression.

� These circuits can be realized by using AND, OR and NOT gates.� Examples: adders, subtractors, code converters, decoders,

encoders, multiplexers, demultiplexers, parity checkers etc.



� Sequential circuit is a logic circuit whose O/P at specified

time is a function of inputs at that time as well as finite number of preceding input.

� Sequential circuit requires Memory element, because its O/P

depends upon present as well as preceding states of elements.

� Basically Sequential circuit is combination of Memory element

and combinational circuit.

� These circuits can be realized by using AND, OR, NOT gatesand flip-flops.

� Examples: registers, counters etc.



Uses:

Two major uses of sequential circuits in digital system are²

� As memories to store information while processing.

� As control circuits to generate control signals

Combinational

Circuit

Memory Element

Inputs

Outputs

Block diagram



Synchronous sequential circuits

� Sequential circuit which employ clock are called as Synchronous

sequential circuits.

� All memory elements are clocked flip-flops.

� Easy to design.

� In digital system mostly synchronous circuits are used.

Asynchronous sequential circuits

� Sequential circuit which do not employ clock are called asunclocked or Asynchronous sequential circuits.

� Difficult to design and hence relatively uncommon.



Half Adder

� A logic circuit which performs addition of two bits is called a half

adder.� A and B are two one bit inputs and which produces sum (S) and

carry (C) with C being the most significant of these two outputs.

Half

Adder

A

B

(C) Carry

(S) Sum



INPUTS OUTPUTS

The Carry output is a simple AND function,

The Sum is an Exclusive-OR.

A B C S

0 0 0 0

0 1 0 1

1 0 0 1

1 1 1 0

� Drawback of half adder is, it doesn¶t cater to carry i.e. it fails

in multi-bit addition.

� It will add A0 and B0, but in next stage we have to add three

bits, which will not be done by the circuit, hence we require aFULL ADDER



Full Adder

� To overcome the drawback of half adder, full adder is designed.� It consider Carry also.

� The logic circuit which can add 3 bits is known as Full Adder.

� The full adder produces a sum and carry value, which are both

binary digits.

� It can be combined with other full adders.



CARRY

IN

input

B

input

A

CARRY

OUT

SUM

digit

0 0 0 0 0

0 0 1 0 1

0 1 0 0 1

0 1 1 1 0

1 0 0 0 1

1 0 1 1 0

1 1 0 1 0

1 1 1 1 1

Truth table for Full Adder



A full adder can be constructed from two half adders by connecting

An and Bn to the input of one half adder, connecting the sum from

that to an input to the second adder, connecting C n-1 to the other input and OR the two carry outputs.

Half

Adder Half

Adder

An

Bn

Cn-1

Carry

Sum Carry

Sum

Cn

Sn



Logic diagram of a Full Adder



R ipple carry adder

--It is a type of multiple bit adder.

--When multiple full adders are used with the carry ins and carry

outs chained together then this is called a ripple carry adder

because the correct value of the carry bit ripples from one bit to the

next--To obtain it n number of full adders are connected.

4-bit ripple carry adder circuit diagram

L6-CombSequAdders

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