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.