Fundamentals of Logic Gates Quiz

The Boolean operation of multiplication is analogous to the logical AND operation. In Boolean algebra, multiplication (often denoted by · or AND) results in 1 only when all inputs are 1. This directly corresponds to the AND gate, which outputs high (1) only when all its inputs are high. The OR gate represents addition, the NOT gate represents inversion, and the XOR gate represents exclusive OR, none of which match multiplication.

An AND gate is defined by its behavior where the output is high (1) only if every input is high. If any input is low (0), the output is low. This contrasts with an OR gate, which outputs high if at least one input is high, a NOT gate, which inverts a single input, and a NOR gate, which outputs high only when all inputs are low.

A NOT gate is commonly called an inverter because it reverses the input signal. If the input is 0, the output is 1, and if the input is 1, the output is 0. This inversion operation is fundamental in digital logic. NAND, OR, and AND gates do not solely perform inversion; NAND combines AND and NOT, but is not exclusively an inverter.

The Boolean expression A + B denotes the logical OR operation. In this expression, the output is 1 if either A or B or both are 1. This matches the function of an OR gate, which outputs high when at least one input is high. An AND gate would be A · B, a NOT gate would be A', and a NAND gate would be (A · B)'.

A NOT gate, or inverter, always produces the opposite value of its input. Since the input is 0, the output must be 1. This is a fundamental property of NOT gates; they are deterministic and never output both values or undefined states for binary inputs.

An OR gate outputs high (1) when at least one of its inputs is high. This is distinct from an AND gate, which requires all inputs to be high, a NAND gate, which outputs low only when all inputs are high, and a NOT gate, which has only one input and inverts it.

A standard NOT gate is designed with a single input and a single output. It inverts the value of that input. Gates like AND or OR can have multiple inputs, but a NOT gate is inherently unary, meaning it only operates on one input.

A three-input OR gate performs the logical OR operation on all three inputs, meaning the output is 1 if at least one of A, B, or C is 1. The expression A + B + C represents this. A · B · C is for an AND gate, (A + B)' is for a NOR gate, and A' is for a NOT gate.

The requirement is that the system is active only when both Door A and Door B are closed, meaning both conditions must be true simultaneously. This is logically an AND operation. An AND gate outputs high only when all inputs are high, so if Door A and Door B sensors send high signals when closed, the AND gate will activate the system only when both are high.

An AND gate outputs 1 only if all inputs are 1. Here, one input is 1 and the other is 0, so the output is 0. The output is not based on a single input; it depends on all inputs. Thus, it is neither the same as the first nor the second input exclusively.

An XOR (exclusive OR) gate outputs 1 when the two inputs are different—one is 0 and the other is 1. If both inputs are the same, the output is 0. An XNOR gate outputs 1 when inputs are the same, an AND gate outputs 1 only when both are 1, and a NOR gate outputs 1 only when both are 0.

An XNOR gate acts as an equality detector; it outputs 1 when both inputs are identical—either both 0 or both 1. If the inputs are different, the output is 0. 'Both high' or 'both low' are subsets of 'the same,' but the correct condition is whenever they are the same, not exclusively both high or both low.

The symbol ⊕ is often used to denote the XOR operation. XOR outputs 1 when inputs A and B are different. This differs from XNOR, which outputs 1 when inputs are the same, NOR, which outputs 1 only when both are 0, and NAND, which outputs 0 only when both are 1.

A NOR gate is the negation of an OR gate. It outputs 1 only when all inputs are 0. If any input is 1, the output is 0. This makes NOR gates useful for functions requiring all-low conditions to activate.

The expression (A ⊕ B)’ typically denotes the XNOR operation, which is the negation of XOR. XNOR outputs 1 when A and B are the same. This is equivalent to (A ⊕ B)', where ⊕ is XOR. Thus, it matches the XNOR gate behavior.