Number Systems

Roman System

Base Numerals and Values

• I : One
• V : Five
• X : Ten
• L :Fifty
• C : Hundred
• D : Five hundred
• M : Thousand

Rules

If a lesser weighted symbol appears to the left of a larger weighted symbol, the lower value is subtracted from the higher value.
Examples : IV (5 -1 = 4), XC (100 – 10 = 90)

If a lesser weighted symbol appears to the right of a larger weighted symbol, the lower value to added to the higher value.
Examples : VII (5 + 1 + 1 = 7), CXX (100 + 10 + 10 = 120)

Drawbacks

Difficult to perform arithmetic operations.

Not easy to read large Roman numbers. Movie companies supposedly use Roman numbers in their copyright dates so that the audience could not quickly figure out if a movie is too old.

Hindu-Arabic System

Digits

In the Decimal system, there are ten digits 1, 2, 3, 4, 5, 6, 7, 8, 9 and most importantly 0 (Zero).

“The Dawn of Nothing” emphasizes the introduction of Zero thereby allowing the positional system of representing numbers.

Advantages

It has several advantages over the Roman Number System.

• Compact representation
• Ease of performing arithmetic operations.

Number systems in Mathematics

• Integers
  Positive, Zero, Negative
• Real Numbers
  Positive, Zero, Negative
• Complex Numbers
  Real Part and Imaginary Part
• …

Bases and Usage

• Base 10 : Decimal
  Most common
• Base 2 : Binary
  Used in computers
• Base 3 : Ternary
• Base 4
• Base 8 : Octal
• Base 16 : Hexadecimal
• Base 60
  Angular and Time Measure
  Minutes & Seconds
• Mixed Base
  Old British Measures
  e.g. Mile, Furlong, Yard, Foot, Inch