Number System Representation

1. Number System Representation
Conversion from Decimal to Binary, Octal, Hexadecimal

2. What Are Number
Systems?
Decimal Number
System
Decimal to Binary
Conclusion
Decimal to Octal Decimal to
Hexa-decimal

3. Number systems are the technique to represent
numbers in the computer system architecture,
every value that you are saving into or getting
from computer memory has a defined number
system. Computer architecture supports
following number systems
• Binary Number System (2 digits)
• Octal Number System (8 digits)
• Decimal Number System (10 digits)
• Hexa-decimal Number System (16 digits)

4. Decimal to Binary
Conversion
Techniques:
• Divide each bit by 2, keep
track of the remainder
• First remainder is bit 0
(LSB, least-significant bit)
• Example =
Decimal number system is the base 10
number system and uses the digits
from 0 to 9. Using these digits you can
express any quantity
12510 11111012
Decimal to Octal
Conversion
Techniques:
• Divide each bit by 8, keep
track of the remainder
• First remainder is bit 0
(LSB, least-significant bit)
• Example =
123410 23228
Decimal to Hexa-
decimal Conversion
Techniques:
• Divide each bit by 16, keep
track of the remainder
• First remainder is bit 0
(LSB, least-significant bit)
• Example =
123410 4𝐷216

8. The language of mathematics is built around the number system - a framework
that allows for the expression and manipulation of numerical values. This system
boasts versatility with its myriad branches, ranging from whole numbers and
decimals to binary code and complex numbers. A deep understanding of the
number system is vital in fields across the board, from mere arithmetic to
intricate computations in areas like computer science and engineering. One
cannot grasp the true essence of mathematical concepts and their applicability
without a thorough immersion in the vastness of the number system.