Quick questions on Binary addition and overflow explained: O-Level Computing

Adding two bits (plus any carry coming in) follows four simple cases:

Start at the rightmost column (the least significant bit) and work left. Add the two digits and any incoming carry, write the result digit, and pass any carry to the next column:

Always confirm a binary addition by converting both numbers and the result to denary. If $a + b$ in denary does not equal the denary value of your binary result, you have dropped a carry somewhere.

A register stores a fixed number of bits, often $8$. An unsigned 8-bit register can hold the values $0$ to $255$, because $2^8 = 256$ patterns. The largest unsigned value is $2^n - 1$ for $n$ bits.

Overflow happens when an addition produces a carry out of the most significant bit, because the result needs more bits than the register has. The extra bit is lost, so the stored answer is wrong. You detect overflow by checking for a carry out of the top column, or by checking whether the true result exceeds $2^n - 1$.

Skipping the denary check is the most common reason a wrong binary sum goes unnoticed.

Add $00001111_2$ and $00000001_2$ and give the 8-bit result. [2 marks]

State the largest value an unsigned 8-bit register can hold, and why. [2 marks]

Add $10000000_2$ and $10000000_2$ in an 8-bit register and explain the result. [3 marks]