Digital Electronics: Logic Gates

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Questions and Answers

What Boolean operation does an inverter perform?

  • NOT (correct)
  • AND
  • OR
  • XOR

If the input to an inverter is HIGH, what will the output be?

  • LOW (correct)
  • HIGH
  • Undefined
  • Floating

What logic gate produces a HIGH output only when all of its inputs are HIGH?

  • OR gate
  • NOR gate
  • AND gate (correct)
  • NAND gate

For a 2-input AND gate, if input A is LOW and input B is HIGH, the output will be:

<p>LOW (B)</p>
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How many possible input combinations are there for a 3-input AND gate?

<p>8 (B)</p>
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Which logic gate's output can be described by the expression X = A + B?

<p>OR (C)</p>
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For a 2-input OR gate, if input A is LOW and input B is HIGH, what will the output be?

<p>HIGH (D)</p>
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In an intrusion detection system using an OR gate, what state must the inputs be in to trigger the alarm?

<p>At least one input HIGH (D)</p>
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Which logic gate produces a LOW output only when all inputs are HIGH?

<p>NAND gate (C)</p>
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A NAND gate is equivalent to which operation?

<p>Negative-OR (C)</p>
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What is the Boolean expression for a 2-input NAND gate?

<p>X = (A * B)Ì… (A)</p>
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Which logic gate produces a LOW output if any input is HIGH?

<p>NOR gate (D)</p>
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For a 2-input NOR gate operating as a negative-AND, what input conditions are required to produce a HIGH output?

<p>Both inputs LOW (D)</p>
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Which logic gate produces a HIGH output only when its inputs are at opposite logic levels?

<p>XOR gate (B)</p>
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The XOR operation can be written as which of the following Boolean expressions?

<p>X = AB + ABÌ… (B)</p>
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In a system with two identical circuits operating in parallel, which gate is used to monitor for a failure, indicated by a HIGH output?

<p>XOR gate (C)</p>
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Which logic gate produces a HIGH output only when both inputs are at the same logic level?

<p>XNOR gate (A)</p>
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Which of the following Boolean expressions represents the XNOR operation?

<p>X = AB + AÌ…BÌ… (D)</p>
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What is the key difference between an XOR and XNOR gate in terms of output?

<p>XOR outputs HIGH if inputs are different; XNOR outputs HIGH if inputs are the same. (A)</p>
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The output of a 2-input gate is HIGH only when one of the inputs is HIGH and the other is LOW. Which type of gate is this?

<p>XOR (B)</p>
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Which gate is functionally equivalent to an inverter followed by an AND gate?

<p>NAND (D)</p>
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If you need a gate that outputs a HIGH signal only when both of its inputs are LOW, which gate should you choose?

<p>NOR (D)</p>
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Which of the following is the correct truth table for a 2-input AND gate?

<p>Inputs: A=0, B=0, Output=0; A=0, B=1, Output=0; A=1, B=0, Output=0; A=1, B=1, Output=1 (A)</p>
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In the expression $X = A \oplus B$, what does the $\oplus$ symbol represent?

<p>XOR (B)</p>
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A 2-input logic gate has the following output waveform: HIGH, LOW, LOW, HIGH. Which gate do you think it is?

<p>XNOR (C)</p>
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Which of the following gates outputs a HIGH output only when all of its inputs are HIGH?

<p>AND (A)</p>
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Regarding logic gates, what is the meaning of the term 'overbar'?

<p>It inverts the entire function. (D)</p>
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Which function is represented in the image?

<p>AND (D)</p>
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Which gate outputs HIGH when A is equal to B?

<p>XNOR (A)</p>
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A gate outputs LOW when at least 1 input is HIGH, which gate is this?

<p>NOR (C)</p>
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Complete the wave form. Given these inputs, what is the output of the XOR function?

<p>Alternating HIGHs and LOWs (B)</p>
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What is an alternative name for the XNOR gate, because of its behavior?

<p>Equivalence gate (A)</p>
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Let's say that Input A is HIGH, but you don't know what Input B is. How do you ensure that the final output of the AND equation is always LOW?

<p>Set B to LOW (C)</p>
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How can you implement the unary NOT function using only 1 NAND gate?

<p>Connect both inputs together (D)</p>
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If you had an AND gate, how would you turn it to a NAND gate with the least modifications?

<p>Add a NOT gate after it (D)</p>
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What is the correct label for this Gate A?

<p>NOR gate (A)</p>
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Flashcards

What is an inverter?

The inverter performs the Boolean NOT operation, inverting the input signal.

How does an inverter work?

When the input is LOW (0), the output is HIGH (1); when the input is HIGH (1), the output is LOW (0).

What is the Boolean expression for an inverter?

The Boolean expression for an inverter is X = Ā, where the overbar indicates the NOT operation (complement).

How does an AND gate work?

The AND gate produces a HIGH (1) output only when all inputs are HIGH (1); otherwise, the output is LOW (0).

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How is the AND operation written?

The AND operation is usually shown with a dot between the variables (A·B) or may be implied (AB).

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How does an OR gate work?

The OR gate produces a HIGH (1) output if any input is HIGH (1); if all inputs are LOW (0), the output is LOW (0).

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How is the OR operation written?

The OR operation is shown with a plus sign (+) between the variables (X = A + B).

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How does a NAND gate work?

The NAND gate produces a LOW (0) output when all inputs are HIGH (1); otherwise, the output is HIGH (1).

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How is the NAND operation written?

The NAND operation is written as X = A·B (with an overbar covering A·B), indicating the NOT of the AND operation.

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A 2-input NOR gate performs a negative-AND operation, when is the output HIGH?

Output X is HIGH only when both input A and input B are LOW.

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How does an XOR gate work?

The XOR gate produces a HIGH (1) output only when both inputs are at opposite logic levels.

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How does an XNOR gate work?

The XNOR gate produces a HIGH (1) output only when both inputs are at the same logic level.

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How is the XOR operation written?

The XOR operation is written as X = ĀB + AĀ or with a circled plus sign X = A ⊕ B.

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How is the XNOR operation written?

The XNOR operation shown as X = ĀB + AB or can be shown with a circled dot between the variables. Thus, it can be shown as X = A ⊙ B.

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Study Notes

  • Digital electronics deals with logic gates.

The Inverter

  • The inverter performs the Boolean NOT operation.
  • If the input is LOW, the output is HIGH.
  • If the input is HIGH, the output is LOW.
  • Boolean expression for an inverter: X = Ä€.
  • A group of inverters can form the 1's complement of a binary number by inverting each bit of the number.

The AND Gate

  • The AND gate produces a HIGH output only when all inputs are HIGH.
  • Otherwise, the output is LOW.
  • The AND operation is written as X = A·B or X = AB.
  • For a 3-input AND gate there are 8 combinations, output is all 0s except when all inputs are 1s.
  • 16 possible input bit combinations for a 4-input AND gate.
  • The output waveform X of the 3-input AND gate is HIGH only when all three input waveforms A, B, and C are HIGH.
  • An AND gate can be used in a seat belt alarm system so the alarm sounds if the ignition is on, the seat belt is unbuckled, and the timer is running.

The OR Gate

  • The OR gate produces a HIGH output if any input is HIGH.
  • If all inputs are LOW, the output is LOW.
  • OR operation is written as X = A + B.
  • When either or both input waveforms are HIGH, the output is HIGH.
  • An OR gate can operate a simplified intrusion detection and alarm system.
  • Magnetic switches produce a high output when open and a low output when closed
  • As long as the windows and the door are secured, the switches are closed and all three of the OR gate inputs are LOW.
  • When one of the windows or the door is opened, a HIGH is produced on that input to the OR gate and the gate output goes HIGH and activates and latches an alarm circuit to warn of the intrusion.

The NAND Gate

  • The NAND gate produces a LOW output when all inputs are HIGH.
  • Otherwise, the output is HIGH.
  • The NAND operation is written as X = A·B. - Alternatively, X = AÌ…BÌ…
  • The output waveform X is LOW only when all three input waveforms are HIGH as shown in the timing diagram.
  • For a 2-input NAND gate performing a negative-OR operation, output X is HIGH when either input A or input B is LOW, or when A and B are LOW.
  • The output waveform X is HIGH any time an input waveform is LOW.

The NOR Gate

  • The NOR gate produces a LOW output if any input is HIGH.
  • If all inputs are HIGH, the output is LOW.
  • The NOR operation is written as X = A + B.
  • The NOR operation produces a LOW if any input is HIGH.
  • For a 2-input NOR gate performing a negative-AND operation, output X is HIGH only when both input A and input B are LOW.
  • A 2-input NOR gate operating as a negative-AND gate is required to produce a HIGH output when both inputs are LOW
  • For the 4-input NOR gate operating as a negative-AND the user should determine the output relative to the inputs.

The XOR gate

  • The XOR gate produces a HIGH output only when both inputs are at opposite logic levels.
  • XOR operation is written as X = Ä€B + AÌ„B
  • Alternatively, it can be written as X = A ⊕ B.
  • An XOR gate can monitor a system containing two identical circuits, detecting a failure if the circuit output is HIGH.
  • The XOR gate produces a HIGH signal only when exactly one input is HIGH.

The XNOR Gate

  • The XNOR gate produces a HIGH output only when both inputs are at the same logic level.
  • The XNOR operation is written as X = AB + AÌ„B
  • Alternatively, it can be written as X = A ⊙ B.
  • The XOR output is HIGH only when both inputs are at opposite levels.
  • The XNOR output is HIGH only when both inputs are the same.

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