**What is Ripple Carry Adder?**

- A ripple carry adder also known as “n-bit parallel adder” is a combinational logic circuit used for the purpose of adding two n-bit binary numbers and requires ‘n’ full adders in the circuit.

**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 A
_{3}A_{2}A_{1}A_{0}and B_{3}B_{2}B_{1}B_{0}will be added as-

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

**Logic Diagram for 4-bit Ripple Carry Adder**

As shown, Ripple Carry Adder works in different stages where the carry out produced by each full adder as output serves as the carry in input for its adjacent most significant full adder. When the carry in becomes available to the full adder, it activates that full adder and it comes into operation.

**Also Read-** **How Full Adder computes the output sum bit and carry bit?**

**Working of a 4-bit Ripple Carry Adder-**

Suppose we want to add two 4 bit binary numbers 0101 (A_{3}A_{2}A_{1}A_{0}) and 1010 (B_{3}B_{2}B_{1}B_{0}). Using ripple carry adder, this addition will be carried out as explained below-

**Stage-01:**

When C_{in} will be fed as input to full Adder A, it will activate full adder A.

Then, At Full Adder A,

- A
_{0}= 1 - B
_{0}= 0 - C
_{in}= 0

The sum bit and carry bit produced as output by full adder A will be calculated by full adder A as-

**Calculating S _{0}–**

S_{0} = A_{0} ⊕ B_{0} ⊕ C_{in}

= 1 ⊕ 0 ⊕ 0

= 1

**∴ S _{0} = 1**

**Calculating C _{0}–**

C_{0} = A_{0}B_{0} ⊕ B_{0}C_{in} ⊕ C_{in}A_{0}

= 1.0 ⊕ 0.0 ⊕ 0.1

= 0 ⊕ 0 ⊕ 0

= 0

**∴ C _{0} = 0**

**Stage-02:**

Now, when C_{o} will be fed as input to full adder B by full adder A, it will activate full adder B.

Then, At Full Adder B,

- A
_{1}= 0 - B
_{1}= 1 - C
_{0}= 0

The sum bit and carry bit produced as output by full adder B will be calculated by full adder B as-

**Calculating S _{1}–**

S_{1} = A_{1} ⊕ B_{1} ⊕ C_{0}

= 0 ⊕ 1 ⊕ 0

= 1

**∴ S _{1} = 1**

**Calculating C _{1}–**

C_{1} = A_{1}B_{1} ⊕ B_{1}C_{0} ⊕ C_{0}A_{1}

= 0.1 ⊕ 1.0 ⊕ 0.0

= 0 ⊕ 0 ⊕ 0

= 0

**∴ C _{1} = 0**

**Stage-03:**

Now, when C_{1} will be fed as input to full adder C by full adder B, it will activate full adder C.

Then, At Full Adder C,

- A
_{2}= 1 - B
_{2}= 0 - C
_{1}= 0

The sum bit and carry bit produced as output by full adder C will be calculated by full adder C as-

**Calculating S _{2}–**

S_{2} = A_{2} ⊕ B_{2} ⊕ C_{1}

= 1 ⊕ 0 ⊕ 0

= 1

**∴ S _{2} = 1**

**Calculating C _{2}–**

C_{2} = A_{2}B_{2} ⊕ B_{2}C_{1} ⊕ C_{1}A_{2}

= 1.0 ⊕ 0.0 ⊕ 0.1

= 0 ⊕ 0 ⊕ 0

= 0

**∴ C _{2} = 0**

**Stage-04:**

Now, when C_{2} will be fed as input to full adder D by full adder C, it will activate full adder D.

Then, At Full Adder D,

- A
_{3}= 0 - B
_{3}= 1 - C
_{2}= 0

The sum bit and carry bit produced as output by full adder D will be calculated by full adder D as-

**Calculating S _{3}–**

S_{3} = A_{3} ⊕ B_{3} ⊕ C_{2}

= 0 ⊕ 1 ⊕ 0

= 1

**∴ S _{3} = 1**

**Calculating C _{3}–**

C_{3} = A_{3}B_{3} ⊕ B_{3}C_{2} ⊕ C_{2}A_{3}

= 0.1 ⊕ 1.0 ⊕ 0.0

= 0 ⊕ 0 ⊕ 0

= 0

**∴ C _{3} = 0**

Thus finally,

- Output Sum = S
_{3}S_{2}S_{1}S_{0}= 1111 - Output Carry = C
_{3 }= 0

**Why Ripple Carry Adder is called so?**

- In Ripple Carry Adder, the carry out produced by each full adder as output serves as the carry in input for its next most significant full adder.
- Since in ripple carry adder, each carry bit ripples or waves into the next stage, that’s why it is called by the name “Ripple Carry Adder”.

**Also Read-** **How Delay is calculated in Ripple Carry Adder?**

**Limitation of Ripple Carry Adder-**

- Ripple Carry Adder does not allow all full adders to be used simultaneously and each full adder has to necessarily wait till the carry bit becomes available from its adjacent less significant full adder.
- This increases the propagation time and due to this reason, ripple carry adder becomes
**extremely slow**which is considered to be the biggest disadvantage of using ripple carry adder.

**Also Read-** **Carry Look Ahead Adder**

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