Computer Science AS CIE
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data-representation as5 主题
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multimedia as3 主题
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compression as2 主题
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networks-and-the-internet as11 主题
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computers-and-components as5 主题
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logic-gates-and-logic-circuits as2 主题
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central-processing-unit-cpu-architecture as6 主题
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assembly-language- as4 主题
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bit-manipulation as1 主题
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operating-systems as3 主题
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language-translators as2 主题
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data-security as3 主题
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data-integrity as1 主题
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ethics-and-ownership as3 主题
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database-concepts as3 主题
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database-management-systems-dbms- as1 主题
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data-definition-language-ddl-and-data-manipulation-language-dml as1 主题
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computational-thinking-skills as1 主题
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algorithms as4 主题
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data-types-and-records as2 主题
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arrays as2 主题
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files as1 主题
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introduction-to-abstract-data-types-adt as1 主题
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programming-basics as1 主题
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constructs as2 主题
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structured-programming as1 主题
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program-development-life-cycle as1 主题
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program-design- as2 主题
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program-testing-and-maintenance as3 主题
logic-construction as
Exam code:9618
From problem statements
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A problem statement is typically a written interpretation of a scenario that requires a specific logical outcome
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Logic circuits can be constructed using from problem statements
Worked Example
A server room has an automatic cooling fan (F)
The fan turns on based on the following input parameters:
|
Parameter |
Description |
Binary Value |
Condition |
|---|---|---|---|
|
T |
Temperature |
1 = Too high |
0 = Acceptable |
|
H |
Humidity |
1 = Too high |
0 = Acceptable |
|
M |
Maintenance mode |
1 = Active |
0 = Inactive |
|
D |
Door sensor |
1 = Door open |
0 = Door closed |
The fan (F = 1) turns on if:
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The temperature is too high
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AND humidity is too high
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AND the door is closed
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UNLESS maintenance mode is active (if maintenance is active, the fan must stay off)
Draw a logic circuit to represent how the fan (F) operates based on the input conditions. [3]
Answer
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NOT gates on D and M inputs [1 mark]
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AND gate combines T AND H or NOT D AND NOT M [1 mark]
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Combines two previous AND outputs (e.g. (T AND H) AND (NOT D AND NOT M)) [1 mark]
From logic expressions
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A logic expression is a way of showing how a logic circuit works using symbols and Boolean logic (AND, OR, NOT)
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It describes the conditions that must be met for the output to be true (1) or false (0)
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From a logic expression, a logic circuit and/or truth table can be constructed
Worked Example
A logic expression is given:
S = (A AND B AND C) OR (B XOR C)
(a) Draw the logic circuit for the given expression [4]
(b) Complete the truth table for the logic expression: [2]
S = (A AND B AND C) OR (B XOR C)
Answer
(a)
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Each correct gate [1 mark]
(b)
|
A |
B |
C |
S |
|---|---|---|---|
|
0 |
0 |
0 |
0 |
|
0 |
0 |
1 |
1 |
|
0 |
1 |
0 |
1 |
|
0 |
1 |
1 |
0 |
|
1 |
0 |
0 |
0 |
|
1 |
0 |
1 |
1 |
|
1 |
1 |
0 |
1 |
|
1 |
1 |
1 |
1 |
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Rows 1 to 4 correct [1 mark]
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Rows 5 to 8 correct [1 mark]
From truth tables
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To create a truth table for the expression P = (A AND B) AND NOT C
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Calculate the numbers of rows needed (2number of inputs)
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In this example there are 3 inputs (A, B, C) so a total of 8 rows are needed (23)
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To not miss any combination of inputs, start with 000 and count up in 3-bit binary (0-7)
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|
A |
B |
C |
|---|---|---|
|
0 |
0 |
0 |
|
0 |
0 |
1 |
|
0 |
1 |
0 |
|
0 |
1 |
1 |
|
1 |
0 |
0 |
|
1 |
0 |
1 |
|
1 |
1 |
0 |
|
1 |
1 |
1 |
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Add a new column to show the results of the brackets first (A AND B)
|
A |
B |
C |
A AND B |
|---|---|---|---|
|
0 |
0 |
0 |
0 |
|
0 |
0 |
1 |
0 |
|
0 |
1 |
0 |
0 |
|
0 |
1 |
1 |
0 |
|
1 |
0 |
0 |
0 |
|
1 |
0 |
1 |
0 |
|
1 |
1 |
0 |
Responses