Binary Addition

Adding binary numbers works like decimal addition: align digits, add column by column, carry when the sum exceeds the base.

Rules: $0 + 0 = 0$, $0 + 1 = 1$, $1 + 0 = 1$, $1 + 1 = 10$ (write 0, carry 1). Example: $1011 + 1101$. Rightmost: $1+1=10$ (write 0, carry 1). Next: $1+0+1=10$ (write 0, carry 1). Next: $0+1+1=10$ (write 0, carry 1). Leftmost: $1+1+1=11$ (write 11). Result: $11000$.

Binary addition is how CPUs perform arithmetic. Every addition in your code becomes a series of binary additions at the hardware level. Understanding this helps you debug overflow bugs and optimize bit manipulations.