2. Signed-magnitude arithmetic

Signed-magnitude arithmetic

Signed addition

Before can before arithmetic with signed-magnitude, we must find and operate on the magnitude as if it was an unsigned binary number.

• If the signs are the same:
  1. Add magnitude to find resutling mangitude.
  2. Sign bit of result will stay the same.
• If they’re different:
  1. Subtract smaller magitude from larger magnitude.
  2. Use sign of operand with larger magntiude for result.

Signed subtraction

We can reduce the complexity of computing binary subtraction, such as in $a-b$, by considering the second operand as a negative number in an addition, by this we can write it as $a+(-b)$. This is relatively cheap to do, as we only need to flip the sign bit, now we can perform signed-magnitude addition on the two resulting operands.

$$\begin{array}{r}(-2)-(-3)=\\ \\ 10010\\ -\underline{10011}\\ \\ \text{is equivalent to}\\ \\ 10010\\ +\underline{00011}\\ 00001\end{array}$$

Signed multiplication / division

• Multiply or divide magnitudes as signed binary.
• Check whether both operands have the same sign:
  • If they are the same: result has positive sign.
  • If not: result has negative sign.