Ripple Carry Adder
 Ripple Carry Adder is a combinational logic circuit.
 It is used for the purpose of adding two nbit binary numbers.
 It requires n full adders in its circuit for adding two nbit binary numbers.
 It is also known as nbit parallel adder.
4bit Ripple Carry Adder
4bit ripple carry adder is used for the purpose of adding two 4bit binary numbers. 
In Mathematics, any two 4bit binary numbers A_{3}A_{2}A_{1}A_{0} and B_{3}B_{2}B_{1}B_{0} 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 carryin as input and produces carryout and sum bit as output.
 The carryout produced by a full adder serves as carryin for its adjacent most significant full adder.
 When carryin 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 4bit Ripple Carry Adder
Let
 The two 4bit numbers are 0101 (A_{3}A_{2}A_{1}A_{0}) and 1010 (B_{3}B_{2}B_{1}B_{0}).
 These numbers are to be added using a 4bit ripple carry adder.
4bit Ripple Carry Adder carries out the addition as explained in the following stages
Stage01:
 When C_{in} is fed as input to the full Adder A, it activates the full adder A.
 Then at full adder A, A_{0} = 1, B_{0} = 0, C_{in} = 0.
Full adder A computes the sum bit and carry bit as
Calculation of S_{0}–
S_{0} = A_{0} ⊕ B_{0} ⊕ C_{in}
S_{0 }= 1 ⊕ 0 ⊕ 0
S_{0 }= 1
Calculation of C_{0}–
C_{0} = A_{0}B_{0} ⊕ B_{0}C_{in} ⊕ C_{in}A_{0}
C_{0} = 1.0 ⊕ 0.0 ⊕ 0.1
C_{0} = 0 ⊕ 0 ⊕ 0
C_{0} = 0
Stage02:
 When C_{0} is fed as input to the full adder B, it activates the full adder B.
 Then at full adder B, A_{1} = 0, B_{1} = 1, C_{0} = 0.
Full adder B computes the sum bit and carry bit as
Calculation of S_{1}–
S_{1} = A_{1} ⊕ B_{1} ⊕ C_{0}
S_{1 }= 0 ⊕ 1 ⊕ 0
S_{1 }= 1
Calculation of C_{1}–
C_{1} = A_{1}B_{1} ⊕ B_{1}C_{0} ⊕ C_{0}A_{1}
C_{1} = 0.1 ⊕ 1.0 ⊕ 0.0
C_{1} = 0 ⊕ 0 ⊕ 0
C_{1} = 0
Stage03:
 When C_{1} is fed as input to the full adder C, it activates the full adder C.
 Then at full adder C, A_{2} = 1, B_{2} = 0, C_{1} = 0.
Full adder C computes the sum bit and carry bit as
Calculation of S_{2}–
S_{2} = A_{2} ⊕ B_{2} ⊕ C_{1}
S_{2} = 1 ⊕ 0 ⊕ 0
S_{2} = 1
Calculation of C_{2}–
C_{2} = A_{2}B_{2} ⊕ B_{2}C_{1} ⊕ C_{1}A_{2}
C_{2} = 1.0 ⊕ 0.0 ⊕ 0.1
C_{2} = 0 ⊕ 0 ⊕ 0
C_{2} = 0
Stage04:
 When C_{2} is fed as input to the full adder D, it activates the full adder D.
 Then at full adder D, A_{3} = 0, B_{3} = 1, C_{2} = 0.
Full adder D computes the sum bit and carry bit as
Calculation of S_{3}–
S_{3} = A_{3} ⊕ B_{3} ⊕ C_{2}
S_{3} = 0 ⊕ 1 ⊕ 0
S_{3} = 1
Calculation of C_{3}–
C_{3} = A_{3}B_{3} ⊕ B_{3}C_{2} ⊕ C_{2}A_{3}
C_{3} = 0.1 ⊕ 1.0 ⊕ 0.0
C_{3} = 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,

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,
Next Article Delay in Ripple Carry Adder
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