Logic gates and Boolean logic

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Notes de leçon

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).

Diapos

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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

Plus de questions

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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