Notes

Addition with unsigned or 2's complement binary numbers

Subtraction with 2's complement binary numbers

Overflow

Extra digits that does NOT fit into the available bits.

Overflow occurs if:

• We get a carry in to sign bit but no carry out

• We get a carry out of the sign bit but no carry in

Overflow never occurs if we add a positive number with a negative number.

• Overflow Example

  

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Sign Extension

• Suppose we have a number which is stored in a four bit register

• We wish to add this number to a number stored in an eight bit register

• We have a device which will do the addition and it is designed to add two 8 bit numbers

• What issues do we need to deal with?

• To add bits to the left of a two’s complement number (i.e. make the number of bits bigger while representing the same numeric value)...
  • Fill the new bits on the left with the value of the sign bit!

• Example

  

Adding a number to itself

$A+A=2\times A=A << 1$

• Examples

  

Questions & Answers

How do you know overflow occurred when adding unsigned numbers?

What are the TWO ways to tell if overflow occurred in 2's complement addition/subtraction?

What is the sum of $101111_2$ and $001010_2$ ?

$111001_2$