Logic gates and Boolean logic

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Boolean logic

Boolean logic works with values True (1) and False (0). Computer circuits are built from logic gates that process binary inputs.

The main gates

NOT (inverter): output is the opposite of the input. NOT 0 = 1; NOT 1 = 0.
AND: output is 1 only if both inputs are 1.
OR: output is 1 if at least one input is 1.
(Some courses also use XOR: output 1 if the inputs are different; and NAND, NOR.)

AND requires both inputs

Truth tables

A truth table lists all input combinations and the output. For two inputs there are 4 rows (00, 01, 10, 11).
AND: 0 0 0 1 (for 00, 01, 10, 11). OR: 0 1 1 1. XOR: 0 1 1 0.

All four input combinations

Combining gates

Gates can be combined into logic diagrams. Q = (A AND B) OR C. For three inputs there are 8 rows.
Write a Boolean expression (A AND B, NOT A) and work out each output step by step.

Q = (A AND B) OR C

Uses

Logic gates are the basis of processors, memory, alarms and decision circuits, e.g. a car alarm sounding if (door open AND ignition off).

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Übungsfragen

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1.What is Boolean logic?
Easy
- Alogic using True and False values
- Blogic using text
- Clogic using colour
- Dlogic using hardware
2.What does a NOT gate do?
Easy
- Ainverts the input
- Badds inputs
- Cchooses the larger
- Dstores a bit
3.What is the output of OR with inputs 0 and 0?
Easy
- A0
- B1
- C10
- Dundefined
4.What is the output of OR with inputs 1 and 0?
Easy
- A1
- B0
- C10
- Dundefined
5.What is the output of AND with inputs 1 and 1?
Easy
- A1
- B0
- C2
- D11
6.What is NOT 1?
Easy
- A0
- B1
- C2
- Dundefined
7.What is the output of XOR with inputs 1 and 1?
Easy
- A0
- B1
- C2
- Dundefined
8.What is the output of XOR with inputs 1 and 0?
Easy
- A1
- B0
- C2
- Dundefined

Mehr Fragen

9.How many rows are in a truth table for 3 inputs?
Easy
- A8
- B6
- C4
- D3
10.How many rows are in a truth table for 2 inputs?
Easy
- A4
- B2
- C8
- D3
11.In the shaped-gate notation used in this lesson, what shape identifies an AND gate?
Easy
- Aa D-shaped gate
- Ba triangle with circle
- Ca curved shield
- Da circle
12.Q = A AND B. If A = 1 and B = 0, what is Q?
Medium
- A0
- B1
- C2
- Dundefined
13.Q = A OR B. If A = 0 and B = 1, what is Q?
Medium
- A1
- B0
- C2
- Dundefined
14.Q = NOT A. If A = 1, what is Q?
Medium
- A0
- B1
- C2
- Dundefined
15.Q = (A AND B) OR C with A=1, B=0, C=1. What is Q?
Medium
- A1
- B0
- C2
- Dundefined
16.Q = NOT (A OR B) with A=0, B=0. What is Q?
Medium
- A1
- B0
- C2
- Dundefined
17.Q = A AND (NOT B) with A=1, B=0. What is Q?
Medium
- A1
- B0
- C2
- Dundefined
18.A car alarm sounds if the door is open AND the ignition is off. If the door is open but the ignition is on, the alarm is:
Medium
- Asilent
- Bsounding
- Cbroken
- Dundefined
19.Q = (A OR B) AND NOT C with A=0, B=1, C=1. What is Q?
Medium
- A0
- B1
- C2
- Dundefined
20.Q = NOT (A AND B) with A=1, B=1. What is Q?
Medium
- A0
- B1
- C2
- Dundefined
21.For which inputs is A OR B equal to 0?
Medium
- Aboth 0
- Bboth 1
- Cone 1
- Dnone
22.For which inputs is A AND B equal to 1?
Medium
- Aboth 1
- Bboth 0
- Cone 1
- Dnone
23.What is a logic diagram?
Easy
- Aa diagram showing gates connected
- Ba flowchart
- Ca graph
- Da map
24.What does '1' mean in Boolean?
Easy
- ATrue or on
- BFalse or off
- Czero
- Derror
25.Which gate gives 1 only when inputs differ?
Medium
- AXOR
- BAND
- COR
- DNOT
26.What is the Boolean expression for 'both A and B'?
Medium
- AA AND B
- BA OR B
- CNOT A
- DA XOR B
27.An AND gate outputs 1 only when both inputs are 1.
Easy
True or false?
28.A NOT gate inverts the input.
Easy
True or false?
29.An OR gate outputs 1 only when both inputs are 1.
Easy
True or false?
30.A truth table for 3 inputs has 8 rows.
Easy
True or false?
31.XOR outputs 1 when inputs are the same.
Medium
True or false?
32.Which are logic gates?
Medium
- AAND
- BOR
- CNOT
- DXOR
- EROM
33.Which outputs equal 1 for inputs A=1, B=0?
Medium
- AA OR B
- BA XOR B
- CNOT B
- DA AND B
- ENOT A
34.Complete the truth table for A AND B (rows 00, 01, 10, 11).
Medium

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