2. Integers

Binary Addition:

$$\begin{array}{r}5\\ +4\\ 9\end{array}$$ $$\begin{array}{r}101\\ +100\\ 1001\end{array}$$

sign | magnitude

0 - positive 1 - negative

operations considering sign (addition to subtraction)

first approach:

if signs are same
	add directly
else 
	find the larger
	subtract the smaller
fix the signs

Is there a better approach?

2’s Complement

3-bit integers (wraps around) $2^3=8$ unique combinations first bit - sign, last two - magnitude 2 + 1 = 3

$$\begin{array}{r}010\\ +001\\ 011\end{array}$$

3 + -2 = 1

$$\begin{array}{r}011\\ +110\\ 1001\end{array}$$

which got the correct answer if u consider first bit as the sign (we are)

Essentially addition but treating the sign bit like a normal bit

Converting signs

1. Flip digits e.g. $101⟹010$

2. Add 1 e.g. $101⟹010⟹011$