NUMBER SYSTEMS (Part 1) Flashcards
Also known as base/radix system
number system
pertains to the number of symbols that is used for counting in a particular number system.
Radix
General format:
𝑑_(𝑛−1) 𝑑_(𝑛−2)…𝑑_1 𝑑_0
Common number systems
- Binary system –
- Decimal system –
- Octal system –
- Hexadecimal system –
base 2 {0,1}
Binary system
base 10 {0-9}
Decimal system
– base 8 {0-7}
Octal system
base 16 {0-9, a-f}
Hexadecimal system
Radix starts from ________ to ________
base 2 to base 36.
USING CONTINUOUS DIVISION OF BASE N FOR INTEGER PART AND CONTINUOUS MULTIPLICATION OF BASE N FOR DECIMAL PART.
Decimal to base n
using positional notation, it is the total sum of 𝑑_𝑛 𝑥 𝑏^𝑛 for 𝑛=0 to 𝑛−1.
Where,
𝑛 – digit position
𝑑_𝑛 – digit representation
𝑏 – radix
base n to Decimal
base 𝑵_𝟏→ DECIMAL → base 𝑵_𝟐
base 𝑵_𝟏 to base 𝑵_𝟐