# 4 bit Binary adder `circuit ` discussion with example.

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.

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. 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

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