MGMT 1000 Lecture 4: MGMT 1000 Lecture 4 Notes
MGMT 1000 Lecture 4 Notes – Counting in different bases
Introduction
• In ancient cultures, the number might have been represented as I or, when in Rome, V
• Similarly, in base 2, the number of oranges is represented as 1012
• And in base 3, the representation looks like this: 123
• The point we are making is that each of the foregoing examples is simply a different way
of representing the same number of oranges.
• You probably already have experience at converting between the standard decimal
number system and Roman numerals.
• Maybe you even wrote a program to do so!
• Once you understand the methods, it is just about as easy to convert between base 10
and the other number bases that we shall use.
• Lets osider ho e out i ase 10, and what each digit means.
• We egi ith sigle digits, … 9
• When we reach 9, we have exhausted all possible single digits in the decimal number
sste; to proeed further, e eted the uers to the s plae:
• It is productive to osider hat the s plae reall eas.
• The s plae sipl represets a out of the uer of ties that e hae led
through the entire group of 10 possible digits.
• Thus, continuing to count, we have 1 group of 10 + 0 more 1 group of 10 + 1 more 1
group of 10 + 2 1 group of 10 + 9 2 groups of 10 + 0 9 groups of 10 + 9
• At this point, we have used all combinations of two digits, and we need to move left
another digit.
• Before we do so, however, we should note that each group shown here represents a
count of 10, since there are 10 digits in the group.
• Thus, the number 43 really refers to 4 × 10 + 3
• The number of oranges is represented as 1012
• And in base 3, the representation looks like this: 123
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