﻿ 4 bit Binary adder circuit / block diagram. Discussion with detailed example. Aritmetic microoperations
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Binary adders are implemented to add two binary numbers. So in order to add two 4 bit binary numbers we need to use 4 full-adders. The connection of full-adders to create bianry adder circuit is discussed in block diagram below.

In this implementation, carry of each full-adder is connected to previous carry.  Detailed discussion on full-adder is covered on this link.
Example

Lets discuss one example for 4 bit binary Adder.  In this example we will use some terms from Register Transfer Level (RTL) implementations.

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

Sol. Load the values in two registers R1 and R2.
So, R1 = 7 (decimal) = 0111 (in binary A3A2A1A0)
&   R2 = 15 (decimal) = 1111 (in binary B3B2B1B0)

So from the above implementation we have -
Stage
Previous carry
Augends bits A
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 and 15 from above table
Is C4S3S2S1S0 = 10110 (In Binary) = 16 (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.