Logic gates and Boolean logic
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レッスンノート
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).
スライド
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練習問題
無料プレビュー — 34問中8問。すべて見るには登録を。
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?
Easy4.What is the output of OR with inputs 1 and 0?
Easy5.What is the output of AND with inputs 1 and 1?
Easy7.What is the output of XOR with inputs 1 and 1?
Easy8.What is the output of XOR with inputs 1 and 0?
Easy
もっと問題
9.How many rows are in a truth table for 3 inputs?
Easy10.How many rows are in a truth table for 2 inputs?
Easy11.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?
Medium13.Q = A OR B. If A = 0 and B = 1, what is Q?
Medium14.Q = NOT A. If A = 1, what is Q?
Medium15.Q = (A AND B) OR C with A=1, B=0, C=1. What is Q?
Medium16.Q = NOT (A OR B) with A=0, B=0. What is Q?
Medium17.Q = A AND (NOT B) with A=1, B=0. What is Q?
Medium18.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?
Medium20.Q = NOT (A AND B) with A=1, B=1. What is Q?
Medium21.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?
Medium26.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.
EasyTrue or false?
28.A NOT gate inverts the input.
EasyTrue or false?
29.An OR gate outputs 1 only when both inputs are 1.
EasyTrue or false?
30.A truth table for 3 inputs has 8 rows.
EasyTrue or false?
31.XOR outputs 1 when inputs are the same.
MediumTrue or false?
32.Which are logic gates?
Medium33.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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