Notes

1. If $a$ is even, then $a + 1 = a \oplus 1$. ($\oplus$ means XOR).
   If $a$ is odd, then $a - 1 = a \oplus 1$.
   • Example 1: \(0110_2 = 6_{10}.\\ 0110_2 + 0001_2 = 0111_2 \quad (6 + 1 = 7);\\ 0110_2 \oplus 0001_2 = 0111_2 \quad (6 \oplus 1 = 7).\)
   • Example 2: \(0111_2 = 7_{10}.\\ 0111_2 + 0001_2 = 1000_2 \quad (7 + 1 = 8);\\ 0111_2 - 0001_2 = 0110_2 \quad (7 - 1 = 6);\\ 0111_2 \oplus 0001_2 = 0110_2 \quad (7 \oplus 1 = 6).\)
2. Quadratic equations: If $\sqrt{b^2-4ac} - b > 0$, \(x_1 = \frac{-b-sign(b)\sqrt{b^2-4ac}}{2a}, x_2 = \frac{-2c}{b+sign(b)\sqrt{b^2-4ac}}.\)