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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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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structured-programming as1 主题
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program-development-life-cycle as1 主题
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binary-arithmetic- as
Exam code:9618
Binary addition
What is binary addition?
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Binary addition involves summing numbers in base-2, which uses only the digits 0 and 1
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Like denary addition, start from the rightmost digit and move towards the left
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Carrying over occurs when the sum of a column is greater than 1, passing the excess to the next left column
Example addition
Worked Example
Add the following two binary integers using binary addition. Show your working. [2]
1 0 0 1 1 0 1 0 + 0 0 1 0 1 1 1 1
Answer
|
carry |
1 |
1 |
1 |
1 |
1 |
|||
|---|---|---|---|---|---|---|---|---|
|
1 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
|
|
+ |
0 |
0 |
1 |
0 |
1 |
1 |
1 |
1 |
|
1 |
1 |
0 |
0 |
1 |
0 |
0 |
1 |
-
1 mark for working [1 mark]
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1 mark for answer [1 mark]
Overflow
What is an overflow?
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Overflow occurs when the sum of two binary numbers exceeds the given number of bits
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In signed number representations, the leftmost bit often serves as the sign bit; overflow can flip this, incorrectly changing the sign of the result
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Overflow generally leads to incorrect or unpredictable results as the extra bits are truncated or wrapped around
Binary subtraction
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To carry out subtraction, the number being subtracted is converted into its negative equivalent using two’s complement
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The two numbers are then added together
Example
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48 – 12
|
-128 |
64 |
32 |
16 |
8 |
4 |
2 |
1 |
||
|---|---|---|---|---|---|---|---|---|---|
|
0 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
= 48 |
|
|
0 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
= 12 |
|
|
find two’s complement of -12 |
|||||||||
|
0 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
= 12 |
|
|
invert |
|||||||||
|
1 |
1 |
1 |
1 |
0 |
0 |
1 |
1 |
||
|
add 1 |
|||||||||
|
1 |
|||||||||
|
result |
|||||||||
|
1 |
1 |
1 |
1 |
0 |
1 |
0 |
0 |
= -12 |
|
|
Add 48 and -12 |
|||||||||
|
-128 |
64 |
32 |
16 |
8 |
4 |
2 |
1 |
||
|
0 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
= 48 |
|
Responses