NKK SWITCHES IS-Dev Kit-8, Руководство пользователя

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IS-Dev Kit-8 User Manual
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IS-Dev Kit 8 Users Manual A.doc
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Appendix
Understanding Decimal, Hexadecimal and Binary Numbers
Decimal is the numbering system we use. It is called base-10. Every digit can be between 0 to 9.
The value of each digit is equal to the digit with ((Digit order) -1) zero in front.
Table 1, Base-10
Value in base-10
Digit x 10000 1000 100 10 1
Multiplication
for converting to
decimal 10
(N-1)
… … 10
4
10
3
10
2
10
1
10
0
Digit order Nth
digit …. …. Fifth
digit Fourth
digit Third
digit Second
digit First
digit
Example: The value of each digit of the Base-10 number 7605 is as follow:
Fourth digit:
7 with (4-1) zero = 7000
Third digit: 6 with (3-1) zero = 600
Second digit: 0 with (2-1) zero = 0
First digit: 5 with (1-1) zero = 5
Numbering system
A numbering system can be based on any number (base-N). However it has to follow the rules:
1. Each digit has to be between 0 to (Base minus one). For example:
---Each digit for Base-2 numbering system can be 0 or 1
---Each digit for Base-5 numbering system can be 0 to 4
---Each digit for base-8 numbering system can be 0 to 7
2. The value of each digit is equal to the digit with ((Digit order) -1) zeros in front.
All the operations that we use on base 10 numbering system such as addition, subtraction, multiplication,
division… works the same for all the numbering systems. The difference is the carry over will be based on the
base-number of the numbering system instead of 10.
Why do we need other base numbering systems?
Computers logic is based on two states:
Yes or No
False or True
High voltage or low voltage