3. Logic Gates & Circuits

Flashcards based on lecture material, made by Gemini 3 Pro.

In the context of digital systems and Boolean algebra, what do the values 1 and 0 represent?

1 represents True/On/High voltage; 0 represents False/Off/Low voltage.

What are the three fundamental Boolean operators?

AND, OR, and NOT.

Which logic gate performs a Boolean multiplication (product)?

The AND gate.

Which logic gate performs a Boolean sum?

The OR gate.

Describe the output condition of an AND gate.

The output is True (1) only if ALL inputs are True (1). Otherwise, it is 0.

Describe the output condition of an OR gate.

The output is True (1) if ANY (at least one) input is True (1). It is 0 only if all inputs are 0.

Describe the output of a NOT gate (Inverter).

The output is the inverse of the input. If input is 1, output is 0; if input is 0, output is 1.

What is the mathematical notation for A AND B?

A · B (or simply AB)

What is the mathematical notation for A OR B?

A + B

What is the mathematical notation for NOT A?

A' or Ā (a bar over the A)

If a logic gate has n inputs, how many rows will its truth table have?

2^n rows.

How is an AND gate constructed using switches (transistors)?

Two switches in series.

How is an OR gate constructed using switches (transistors)?

Two switches in parallel.

What does the XOR (Exclusive OR) gate output?

It outputs True (1) if one and only one of its inputs is True. (i.e., inputs are different). If inputs are the same, output is 0.

What is the symbol for XOR?

A ⊕ B

What is a NAND gate?

NOT AND. It behaves like an AND gate followed by a NOT gate. Output is 0 only if all inputs are 1.

What is a NOR gate?

NOT OR. It behaves like an OR gate followed by a NOT gate. Output is 1 only if all inputs are 0.

Why are NAND and NOR gates called ""Universal Gates""?

Because any other logic function (AND, OR, NOT) can be built using only NAND or only NOR gates.

What is a Combinational Circuit?

A circuit where the output depends only on the current combination of inputs. It has no memory of past states.

Give two examples of Combinational Circuits.

Adders, Multiplexers (MUX), ALUs, Encoders/Decoders.

What is a Sequential Circuit?

A circuit where the output depends on the current inputs AND the previous state (past outputs). It possesses memory.

What structural feature allows Sequential Circuits to have memory?

Feedback (looping the output back to the input).

What is a Sum-of-Products (SOP) expression?

A Boolean expression where several product terms (ANDed variables) are added together (ORed). E.g., F = AB + A'C.

How do you derive an SOP expression from a Truth Table?

Identify every row where the Output is 1. Create an AND term for that row (negating inputs that are 0), then OR all these terms together.

What is a Multiplexer (MUX)?

A combinational circuit that selects one of several input signals and forwards the selected input into a single line based on control/select lines.

What is an SR Flip-Flop (Latch)?

A basic sequential circuit made of two cross-coupled NOR (or NAND) gates that can store one bit of data (Set or Reset).

In an SR Flip-Flop made of NOR gates, what happens if S=1 and R=0?

The output Q becomes 1 (Set state).

In an SR Flip-Flop made of NOR gates, what happens if S=0 and R=1?

The output Q becomes 0 (Reset state).

In an SR Flip-Flop made of NOR gates, what happens if S=0 and R=0?

The circuit maintains its previous state (Memory/Hold).

What is the ""Invalid"" or ""Undefined"" state of an SR Flip-Flop (NOR version)?

When S=1 and R=1 simultaneously. This causes instability/race conditions.

What is a Clock in digital circuits?

A signal that oscillates between high and low states, used to synchronize the timing of state changes in sequential circuits.

What is a Clocked SR Flip-Flop?

An SR flip-flop that includes a clock input. It only changes state when the clock signal permits (e.g., is high or on a specific edge).

What is a D Flip-Flop?

A modified flip-flop with a Data (D) input and a Clock (C) input. It captures the value of D when the clock triggers.

Why is a D Flip-Flop often preferred over a standard SR Flip-Flop?

It removes the indeterminate (invalid) state found in SR flip-flops by ensuring inputs are never contradictory.

What is a Register?

A group of flip-flops (usually D flip-flops) arranged to store multiple bits of data (e.g., a 4-bit register stores 4 bits).

Visually, which logic gate looks like a letter 'D'?

The AND gate.

Visually, which logic gate looks like a curved shield or arrow head?

The OR gate.

Visually, how is a NOT gate distinguished from a buffer?

By the small circle (bubble) at the output tip of the triangle.

If a Sequential Circuit has inputs A=0, B=0, Output Q=1, and setting B=1 changes Q to 0, which input is likely the 'Reset'?

Input B.

What is a 'Race Condition' in the context of latches?

When the output depends on which of two inputs changes fastest or reaches the gate first, often leading to unpredictable behavior (occurring in the S=1, R=1 state