(4)Addition and subtraction of binary numbers
To add or subtract binary numbers, arrange the digits in the same way as
decimal numbers, and calculate from the last digits.
●Addition
During addition, digits must be carried over so that “(1)2 + (1)2 = (10)2.”
Example
Calculate (1001)2 + (011)2
1 1 Digits carried over
( 1001 ) 2
( 011 ) 2
+
( 1100 ) 2
●Subtraction
During subtraction, digits must be carried over so that “(10)2 − (1)2 = (1)2.”
Example
Calculate (1001)2 − (011)2
0 1 Digits carried over
( 1001 ) 2
− ( 011 ) 2
( 110 ) 2
2
Set
A “set” is a collection of data grouped following certain well-defined conditions.
Using sets, it is possible to express written text such as “A OR B.” These
types of statements are known as “propositions.”
Sets expressed through propos itions can be graphically represented by
“Venn diagrams.”
The relationship between three typical kinds of sets and Venn diagrams is
shown below.
Set
Venn
diagram
A OR B (A + B)
A
B
A AND B (A & B)
A
B
NOT A (¬A)
A
In order to interpret these Venn diagrams, the “truth-value” is required.
For the “truth-value,” a value of “1” indicates “True,” and a value of “0”
indicates “False.”
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