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Overflow in Binary Arithmetic.  Discussion with examples.
Overflow Introduction and scenarios
In terms of computing, two  numbers are loaded into registers before performing any arithmetic operations.  For a number between 0 to 15 we can use a register of length 4 bits.  When two 4 bit numbers are added and the result is greater than 4 bits then we get an overflow condition..

Overflow can occur in either of the two following scenarios:-

Adding two positive numbers.
Or, Adding two negative numbers in signed arithmetic.
Example1 - Add 2 unsigned binary numbers.
Add two binary numbers 10 and 15 with previous carry = 0.

Sol. Load the values in two registers R1 and R2.

So, R1 = 10 (decimal) = 1010 (in binary A3A2A1A0)
&   R2 = 15 (decimal) = 1111 (in binary B3B2B1B0)

So from the binary adder implementation.


Refer binary adder example for detailed calculations.
Result = (Carry = 1) (Sum = 1001)





In this case Overflow is true and result includes the overflow bit. We can use a separate flip-flop to store the result of overflow condition.
Example3 - Add 2 signed number to not produce overflow.
Example2 - Add 2 signed number to produce overflow.
Overflow can never occur when adding a positive number to a negative number. The reason being the result is always smaller than the original larger number. We will discuss the overflow condition with examples below:-  
Interview Questions.

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Interview Questions. Main, FPGA, Digital Fundamentals