Explain the range of numbers in two's complement for n bits and demonstrate adding 63 and -64 using 7 bits in 2's complement.

1.a.i) Range of numbers in two's complement for $n$ bits
The range of numbers that can be represented in $n$-bit two's complement is from $-2^{n-1}$ to $2^{n-1} - 1$.

$$\boxed{-2^{n-1} \text{ to } 2^{n-1} - 1}$$

1.a.ii) Add 63 and -64 using 7 bits in 2's complement

Step 1: Convert 63 to 7-bit binary.

$$63_{10} = 0111111_2$$

Step