Computer-science_A-level_Cie
-
computers-and-components6 主题
-
logic-gates-and-logic-circuits2 主题
-
central-processing-unit-cpu-architecture6 主题
-
assembly-language-4 主题
-
bit-manipulation1 主题
-
operating-systems3 主题
-
language-translators2 主题
-
data-security3 主题
-
data-integrity1 主题
-
ethics-and-ownership3 主题
-
database-concepts3 主题
-
database-management-systems-dbms-1 主题
-
data-definition-language-ddl-and-data-manipulation-language-dml1 主题
-
computational-thinking-skills1 主题
-
algorithms14 主题
-
data-types-and-records2 主题
-
arrays2 主题
-
files1 主题
-
introduction-to-abstract-data-types-adt1 主题
-
programming-basics1 主题
-
constructs2 主题
-
structured-programming1 主题
-
program-development-life-cycle2 主题
-
program-design-2 主题
-
program-testing-and-maintenance3 主题
-
user-defined-data-types1 主题
-
file-organisation-and-access-3 主题
-
floating-point-numbers-representation-and-manipulation3 主题
-
protocols2 主题
-
circuit-switching-packet-switching1 主题
-
processors-parallel-processing-and-virtual-machines5 主题
-
boolean-algebra-and-logic-circuits4 主题
-
purposes-of-an-operating-system-os3 主题
-
translation-software3 主题
-
encryption-encryption-protocols-and-digital-certificates3 主题
-
artificial-intelligence-ai4 主题
-
recursion1 主题
-
programming-paradigms4 主题
-
object-oriented-programming7 主题
-
file-processing-and-exception-handling2 主题
-
data-representation5 主题
-
multimedia3 主题
-
compression2 主题
-
networks-and-the-internet11 主题
binary-arithmetic
Binary addition
What is binary addition?
-
Binary addition involves summing numbers in base-2, which uses only the digits 0 and 1
-
Like denary addition, start from the rightmost digit and move towards the left
-
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]
-
1 mark for answer [1 mark]
Overflow
What is an overflow?
-
Overflow occurs when the sum of two binary numbers exceeds the given number of bits
-
In signed number representations, the leftmost bit often serves as the sign bit; overflow can flip this, incorrectly changing the sign of the result
-
Overflow generally leads to incorrect or unpredictable results as the extra bits are truncated or wrapped around
Binary subtraction
-
To carry out subtraction, the number being subtracted is converted into its negative equivalent using two’s complement
-
The two numbers are then added together
Example
-
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