Step 1: State the condition to be satisfied.
We need to identify which logic gates produce a HIGH (1) output when ALL inputs are LOW (0). Let us examine the truth table of each relevant gate for two inputs.
Step 2: Analyse the NOR gate.
The NOR gate is the complement of the OR gate. Its output is HIGH only when ALL inputs are LOW. For inputs $A = 0, B = 0$: output $Y = 1$. For any other input combination, $Y = 0$. So the NOR gate satisfies our condition.
Step 3: Analyse the NAND gate.
The NAND gate is the complement of the AND gate. The AND gate gives output 0 when any input is 0; therefore the NAND gate gives output 1 when any input is 0. In particular, when ALL inputs are 0, the NAND output is 1. For $A = 0, B = 0$: NAND output $Y = 1$. So NAND also satisfies our condition.
Step 4: Analyse the AND gate.
The AND gate gives HIGH output only when ALL inputs are HIGH. When all inputs are LOW ($A = 0, B = 0$), AND output is 0. So AND does not satisfy the condition.
Step 5: Analyse the OR gate.
The OR gate gives HIGH output when at least one input is HIGH. When all inputs are LOW, OR output is 0. So OR does not satisfy the condition.
Step 6: Conclude the answer.
Only NOR and NAND gates produce a HIGH output when all inputs are LOW. \[ \boxed{\text{NOR and NAND}} \]