# Hardware Design Question: **Download Questions PDF**

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## What are the different Adder circuits you studied?

## Answers:

Adders are generally of five types:

1) Ripple Carry Adder:

The Ripple carry adder(RCA) consists of a building block named Half

Adder(HA) which is cascaded to form a Full Adder(FA). These building

blocks HAs and FAs are also the building blocks of all types of

adders.The n full adders are cascaded to form n bit RCA.

The full adder has three input pins(input Ai,input Bi,carryin Ci) and

two output pins(Sum and Ci+1).Its equations are:

Sum=Ai^Bi^Ci

Ci+1=Ai.Bi+Bi.Ci+Ai.Ci

2)Carry Lookahead Adder:

The Carry Lookahead Adder(CLA) reduces the delay as that in RCA. Let

Gi=Ai.Bi, and Pi=Ai^Bi, then Ci+1=Gi+Pi.Ci.

The expressions for Sum and Ci+1 is then defined completely in terms of

input pins rather wait for input carry to appear.

3)Carry Select Adder:

The carry select adder uses duplicate modules for each combination of

input carry(i.e. 1 and 0).The multiplexers then select the appropriate

sum and carry output according to the carry output of the preceding

stages.

1) Ripple Carry Adder:

The Ripple carry adder(RCA) consists of a building block named Half

Adder(HA) which is cascaded to form a Full Adder(FA). These building

blocks HAs and FAs are also the building blocks of all types of

adders.The n full adders are cascaded to form n bit RCA.

The full adder has three input pins(input Ai,input Bi,carryin Ci) and

two output pins(Sum and Ci+1).Its equations are:

Sum=Ai^Bi^Ci

Ci+1=Ai.Bi+Bi.Ci+Ai.Ci

2)Carry Lookahead Adder:

The Carry Lookahead Adder(CLA) reduces the delay as that in RCA. Let

Gi=Ai.Bi, and Pi=Ai^Bi, then Ci+1=Gi+Pi.Ci.

The expressions for Sum and Ci+1 is then defined completely in terms of

input pins rather wait for input carry to appear.

3)Carry Select Adder:

The carry select adder uses duplicate modules for each combination of

input carry(i.e. 1 and 0).The multiplexers then select the appropriate

sum and carry output according to the carry output of the preceding

stages.

4)Carry Skip Adder:

The carry skip adder are as fast as carry lookahead adders which are

the fastest adders but its speed decreases to about 20-30% if input

operands are 64-bit or more. In these adders we divide the input bit

stream into various blocks and make use of two observations:

-if each element of the two bit streams are unequal,i.e. Ai!=Bi than

the carry input of the block is equal to the carry input.

-if each element of the two bit streams are equal,i.e. Ai=Bi than the

carry input of the block is opposite of the carry input.

5)Carry Save Adder:

The carry save adder reduces the addition of three elements into

addition of two elements,i.e. if you want sum of nine numbers it

reduces it into sum of six numbers. In first step the sum of three

numbers is calculated without bothering for the carry.During the second

step only carry is calculated which is then added to the generated sum

to give the required sum.

The carry skip adder are as fast as carry lookahead adders which are

the fastest adders but its speed decreases to about 20-30% if input

operands are 64-bit or more. In these adders we divide the input bit

stream into various blocks and make use of two observations:

-if each element of the two bit streams are unequal,i.e. Ai!=Bi than

the carry input of the block is equal to the carry input.

-if each element of the two bit streams are equal,i.e. Ai=Bi than the

carry input of the block is opposite of the carry input.

5)Carry Save Adder:

The carry save adder reduces the addition of three elements into

addition of two elements,i.e. if you want sum of nine numbers it

reduces it into sum of six numbers. In first step the sum of three

numbers is calculated without bothering for the carry.During the second

step only carry is calculated which is then added to the generated sum

to give the required sum.

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