4 bit Binary adder circuit discussion with example.

4 bit Binary Adder introduction:

Binary adders are implemented to add two binary numbers. So in order to add two 4 bit binary numbers, we will need to use 4 full-adders. The connection of full-adders to create binary adder circuit is discussed in block diagram below. 

In this implementation, carry of each full-adder is connected to previous carry.

Lets start with the expressions for the FULL ADDER :-
Sum_out = [(in_x) XOR (in_y)] XOR [(carry_in)]
Carry_out = [(in_x) AND (in_y)] OR [ (in_x XOR in_y) AND carry_in ]

Next we will draw the circuit of 4 Bit Binary Adder

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Circuit of 4 Bit Binary Adder consisits of a sequence of full-adders. Details below with circuit and a truth-table.

4 Bit Binary Adder Circuit.

We will need to discuss an Example to understand this in more details. In this example we will use some terms from Register Transfer Level (RTL) implementations. Understand more about RTL.

Problem: Add two binary numbers 7 and 15 with previous carry = 0.

Solution: Load the values into registers R1 and R2. 
So, R1 = 7 (decimal) = 0111 (in binary A3A2A1A0)
&   R2 = 15 (decimal) = 1111 (in binary B3B2B1B0)
Lets implement a table and then continue...

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Stage  Previous carry  Augends bits A  Addend bits B Sum Next carry
0 C0=0 A0=1 B0=1 S0=0 C1=1
1 C1=1 A1=1 B1=1 S1=1 C2=1
2 C2=1 A2=1 B2=1 S2=1 C3=1
3 C3=1 A3=0 B3=1 S3=0 C4=1

Sum of two binary numbers 7 & 15 from above table
Is C4S3S2S1S0 = 10110 (In Binary) = 16+4+2 = 22 ( in decimal)

In the results we have appended C4 in front of the sum digits to accommodate overflow bit from the binary addition flow. Overflow is discussed in this section.

Detailed discussion on full-adder is covered on this link.

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