Ripple Carry Adder | 4 bit Ripple Carry Adder

Ripple Carry Adder-

 

  • Ripple Carry Adder is a combinational logic circuit.
  • It is used for the purpose of adding two n-bit binary numbers.
  • It requires n full adders in its circuit for adding two n-bit binary numbers.
  • It is also known as n-bit parallel adder.

 

4-bit Ripple Carry Adder-

 

4-bit ripple carry adder is used for the purpose of adding two 4-bit binary numbers.

 

In Mathematics, any two 4-bit binary numbers A3A2A1A0 and B3B2B1B0 are added as shown below-

 

 

Using ripple carry adder, this addition is carried out as shown by the following logic diagram-

 

 

As shown-

  • Ripple Carry Adder works in different stages.
  • Each full adder takes the carry-in as input and produces carry-out and sum bit as output.
  • The carry-out produced by a full adder serves as carry-in for its adjacent most significant full adder.
  • When carry-in becomes available to the full adder, it activates the full adder.
  • After full adder becomes activated, it comes into operation.

 

Also Read- Full Adder Working

 

Working Of 4-bit Ripple Carry Adder-

 

Let-

  • The two 4-bit numbers are 0101 (A3A2A1A0) and 1010 (B3B2B1B0).
  • These numbers are to be added using a 4-bit ripple carry adder.

 

4-bit Ripple Carry Adder carries out the addition as explained in the following stages-

 

Stage-01:

 

  • When Cin is fed as input to the full Adder A, it activates the full adder A.
  • Then at full adder A, A0 = 1, B0 = 0, Cin = 0.

 

Full adder A computes the sum bit and carry bit as-

 

Calculation of S0

 

S0 = A0 ⊕  B0 ⊕ Cin

S0 = 1 ⊕ 0 ⊕ 0

S0 = 1

 

Calculation of C0

 

C0 = A0B0 ⊕  B0Cin ⊕ CinA0

C0 = 1.0 ⊕ 0.0 ⊕ 0.1

C0 = 0 ⊕ 0 ⊕ 0

C0 = 0

 

Stage-02:

 

  • When C0 is fed as input to the full adder B, it activates the full adder B.
  • Then at full adder B, A1 = 0, B1 = 1, C0 = 0.

 

Full adder B computes the sum bit and carry bit as-

 

Calculation of S1

 

S1 = A1 ⊕  B1 ⊕ C0

S1 = 0 ⊕ 1 ⊕ 0

S1 = 1

 

Calculation of C1

 

C1 = A1B1 ⊕  B1C0 ⊕ C0A1

C1 = 0.1 ⊕ 1.0 ⊕ 0.0

C1 = 0 ⊕ 0 ⊕ 0

C1 = 0

 

Stage-03:

 

  • When C1 is fed as input to the full adder C, it activates the full adder C.
  • Then at full adder C, A2 = 1, B2 = 0, C1 = 0.

 

Full adder C computes the sum bit and carry bit as-

 

Calculation of S2

 

S2 = A2 ⊕  B2 ⊕ C1

S2 = 1 ⊕ 0 ⊕ 0

S2 = 1

 

Calculation of C2

 

C2 = A2B2 ⊕  B2C1 ⊕ C1A2

C2 = 1.0 ⊕ 0.0 ⊕ 0.1

C2 = 0 ⊕ 0 ⊕ 0

C2 = 0

 

Stage-04:

 

  • When C2 is fed as input to the full adder D, it activates the full adder D.
  • Then at full adder D, A3 = 0, B3 = 1, C2 = 0.

 

Full adder D computes the sum bit and carry bit as-

 

Calculation of S3

 

S3 = A3 ⊕  B3 ⊕ C2

S3 = 0 ⊕ 1 ⊕ 0

S3 = 1

 

Calculation of C3

 

C3 = A3B3 ⊕  B3C2 ⊕ C2A3

C3 = 0.1 ⊕ 1.0 ⊕ 0.0

C3 = 0 ⊕ 0 ⊕ 0

C3 = 0

 

Thus finally,

  • Output Sum = S3S2S1S0 = 1111
  • Output Carry = C= 0

 

Why Ripple Carry Adder is Called So?

 

In Ripple Carry Adder,

  • The carry out produced by each full adder serves as carry-in for its adjacent most significant full adder.
  • Each carry bit ripples or waves into the next stage.
  • That’s why, it is called as “Ripple Carry Adder”.

 

Disadvantages of Ripple Carry Adder-

 

  • Ripple Carry Adder does not allow to use all the full adders simultaneously.
  • Each full adder has to necessarily wait until the carry bit becomes available from its adjacent full adder.
  • This increases the propagation time.
  • Due to this reason, ripple carry adder becomes extremely slow.
  • This is considered to be the biggest disadvantage of using ripple carry adder.

 

To overcome this disadvantage, Carry Look Ahead Adder comes into play.

 

To gain better understanding about Ripple Carry Adder,

Watch this Video Lecture

 

Next Article- Delay in Ripple Carry Adder

 

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Watch video lectures by visiting our YouTube channel LearnVidFun.

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Ripple Carry Adder | 4 bit Ripple Carry Adder
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Ripple Carry Adder | 4 bit Ripple Carry Adder
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Ripple carry adder is a combinational logic circuit used for the purpose of adding two n-bit binary numbers. 4-bit ripple carry adder is used for adding two 4-bit binary numbers. N-bit ripple carry adder is used for adding two N-bit binary numbers.
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Gate Vidyalay
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