A logic gate is a visual way of representing a Boolean expression .

Name the six logic gates covered in this course.

AND , OR , NOT , XOR , NAND and NOR .

When does an AND gate return TRUE?

Only if both inputs are TRUE ; otherwise it returns FALSE.

When does an OR gate return TRUE?

If either input is TRUE ; it returns FALSE only when both inputs are FALSE .

What does a NOT gate do?

It reverses the input value — NOT TRUE gives FALSE, and NOT FALSE gives TRUE.

When does an XOR gate return TRUE?

If either input is TRUE but NOT both — so TRUE XOR TRUE gives FALSE .

When does a NAND gate return TRUE?

If either or both inputs are FALSE — it returns FALSE only when both inputs are TRUE .

When does a NOR gate return TRUE?

Only if both inputs are FALSE .

A truth table is a tool used to visualise the results of Boolean expressions , representing all possible inputs and the associated outputs .

Give the output column of a two-input AND gate for inputs 00, 01, 10, 11.

0, 0, 0, 1 — only 1 when both inputs are 1.

Give the output column of a two-input OR gate for inputs 00, 01, 10, 11.

0, 1, 1, 1 — only 0 when both inputs are 0.

Give the output column of a two-input XOR gate for inputs 00, 01, 10, 11.

0, 1, 1, 0 — 1 only when the two inputs differ.

Give the output column of a two-input NAND gate for inputs 00, 01, 10, 11.

1, 1, 1, 0 — the exact opposite of AND.

The output column of a two-input NOR gate for 00, 01, 10, 11 is 1, 0, 0, .

The output column of a two-input NOR gate for 00, 01, 10, 11 is 1, 0, 0, 0 .

True or False? An XOR gate and an OR gate give the same output when both inputs are 1.

False. With both inputs 1, OR gives 1 but XOR gives 0 , because XOR is TRUE only when the inputs differ.

Define problem statement .

A problem statement is a written interpretation of a scenario that requires a specific logical outcome , from which a logic circuit can be constructed.

Define logic expression .

A logic expression shows how a logic circuit works using symbols and Boolean logic , describing the conditions that must be met for the output to be true (1) or false (0) .

What two things can be constructed from a logic expression?

A logic circuit and a truth table .

How do you calculate the number of rows needed in a truth table?

2 to the power of the number of inputs , so three inputs need 8 rows .

To avoid missing an input combination, start at 000 and count up in -bit binary.

To avoid missing an input combination, start at 000 and count up in 3 -bit binary.

Why add intermediate columns to a truth table?

They show the results of the brackets first , which supports the process , though they can be skipped if you can do those steps in your head.

For which single input combination is P = (A AND B) AND NOT C equal to 1?

Only when A = 1, B = 1 and C = 0 , because A AND B must be 1 and NOT C must be 1.

Why is P = (A AND B) AND NOT C equal to 0 when A, B and C are all 1?

A AND B gives 1 , but NOT C gives 0 , so the final AND produces 0 .

For S = (A AND B AND C) OR (B XOR C), what is S when A=0, B=1, C=1?

0 — A AND B AND C gives 0 because A is 0, and B XOR C gives 0 because B and C are the same, so the OR produces 0.

For S = (A AND B AND C) OR (B XOR C), what is S when A=1, B=1, C=1?

1 — B XOR C gives 0, but A AND B AND C gives 1 , so the OR produces 1.

What can be created from a logic circuit?

The logic expression and the truth table .

A fan turns on when temperature and humidity are both too high, the door is closed, and maintenance mode is off. Write the logic expression.

F = (T AND H) AND (NOT D AND NOT M) , where NOT D means the door is closed and NOT M means maintenance is inactive.

Why do the door and maintenance inputs need NOT gates in that fan circuit?

Because the fan must run when the door is closed (D = 0) and when maintenance is inactive (M = 0) , so both inputs must be inverted before the AND.

True or False? A truth table for a Boolean expression must always include a column for every intermediate step.

False. It is possible to create a truth table showing only the inputs and the final outputs ; the extra columns support the process but can be skipped.

A LevelComputer ScienceCambridge (CIE)Flashcards3. HardwareLogic Gates & Logic Circuits

Logic Gates & Logic Circuits (Cambridge (CIE) A Level Computer Science): Flashcards

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Cards in this collection (29)

Define logic gate.
A logic gate is a visual way of representing a Boolean expression.
Name the six logic gates covered in this course.
AND, OR, NOT, XOR, NAND and NOR.
When does an AND gate return TRUE?
Only if both inputs are TRUE; otherwise it returns FALSE.
When does an OR gate return TRUE?
If either input is TRUE; it returns FALSE only when both inputs are FALSE.
What does a NOT gate do?
It reverses the input value — NOT TRUE gives FALSE, and NOT FALSE gives TRUE.
When does an XOR gate return TRUE?
If either input is TRUE but NOT both — so TRUE XOR TRUE gives FALSE.
When does a NAND gate return TRUE?
If either or both inputs are FALSE — it returns FALSE only when both inputs are TRUE.
When does a NOR gate return TRUE?
Only if both inputs are FALSE.
Define truth table.
A truth table is a tool used to visualise the results of Boolean expressions, representing all possible inputs and the associated outputs.
Give the output column of a two-input AND gate for inputs 00, 01, 10, 11.
0, 0, 0, 1 — only 1 when both inputs are 1.
Give the output column of a two-input OR gate for inputs 00, 01, 10, 11.
0, 1, 1, 1 — only 0 when both inputs are 0.
Give the output column of a two-input XOR gate for inputs 00, 01, 10, 11.
0, 1, 1, 0 — 1 only when the two inputs differ.
Give the output column of a two-input NAND gate for inputs 00, 01, 10, 11.
1, 1, 1, 0 — the exact opposite of AND.
The output column of a two-input NOR gate for 00, 01, 10, 11 is 1, 0, 0, .
The output column of a two-input NOR gate for 00, 01, 10, 11 is 1, 0, 0, 0.
True or False?
An XOR gate and an OR gate give the same output when both inputs are 1.
False.
With both inputs 1, OR gives 1 but XOR gives 0, because XOR is TRUE only when the inputs differ.
Define problem statement.
A problem statement is a written interpretation of a scenario that requires a specific logical outcome, from which a logic circuit can be constructed.
Define logic expression.
A logic expression shows how a logic circuit works using symbols and Boolean logic, describing the conditions that must be met for the output to be true (1) or false (0).
What two things can be constructed from a logic expression?
A logic circuit and a truth table.
How do you calculate the number of rows needed in a truth table?
2 to the power of the number of inputs, so three inputs need 8 rows.
To avoid missing an input combination, start at 000 and count up in -bit binary.
To avoid missing an input combination, start at 000 and count up in 3-bit binary.
Why add intermediate columns to a truth table?
They show the results of the brackets first, which supports the process, though they can be skipped if you can do those steps in your head.
For which single input combination is P = (A AND B) AND NOT C equal to 1?
Only when A = 1, B = 1 and C = 0, because A AND B must be 1 and NOT C must be 1.
Why is P = (A AND B) AND NOT C equal to 0 when A, B and C are all 1?
A AND B gives 1, but NOT C gives 0, so the final AND produces 0.
For S = (A AND B AND C) OR (B XOR C), what is S when A=0, B=1, C=1?
0 — A AND B AND C gives 0 because A is 0, and B XOR C gives 0 because B and C are the same, so the OR produces 0.
For S = (A AND B AND C) OR (B XOR C), what is S when A=1, B=1, C=1?
1 — B XOR C gives 0, but A AND B AND C gives 1, so the OR produces 1.
What can be created from a logic circuit?
The logic expression and the truth table.
A fan turns on when temperature and humidity are both too high, the door is closed, and maintenance mode is off. Write the logic expression.
F = (T AND H) AND (NOT D AND NOT M), where NOT D means the door is closed and NOT M means maintenance is inactive.
Why do the door and maintenance inputs need NOT gates in that fan circuit?
Because the fan must run when the door is closed (D = 0) and when maintenance is inactive (M = 0), so both inputs must be inverted before the AND.
True or False?
A truth table for a Boolean expression must always include a column for every intermediate step.
False.
It is possible to create a truth table showing only the inputs and the final outputs; the extra columns support the process but can be skipped.

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