Sistema de numeración en electronica

Numeration systems
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Questions
Question 1
The numeration system we use in our daily lives is called base ten, also called decimal or denary. What,
exactly, does ”base ten” mean?
Given the following base-ten number, identify which digitsoccupy the ”one’s place,” ”ten’s place,”
”hundred’s place,” and ”thousand’s place,” respectively:
5, 183
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Question 2
Observe the following sequence of numbers:
00
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
.
.
.
What pattern(s) do you notice in the digits, as we count upward from 0 to 21 (and beyond)? This may
seem like a very simplisticquestion (and it is!), but it is important to recognize any inherent patterns so
that you may understand counting sequences in numeration systems with bases other than ten.
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Question 3
The ancient Mayans used a vigesimal, or base-twenty, numeration system in their mathematics. Each
”digit” was a actually a composite of dots and/or lines, as such:

Zero

One

Two

ThreeFour

Five

Six

Seven

Eight

Nine

Ten

Eleven

Twelve

Fifteen

Sixteen

Seventeen

Thirteen

Eighteen

Fourteen

Nineteen

To represent numbers larger than twenty, the Mayans combined multiple ”digits” the same way we do
to represent numbers larger than ten. For example:

Twenty

Twenty six

Forty eight

Seventy one

Four hundred nineteen

Based onthe examples shown above, determine the place-weighting of each ”digit” in the vigesimal
numeration system. For example, in our denary, or base-ten, system, we have a one’s place, a ten’s place,
a hundred’s place, and so on, each successive ”place” having ten times the ”weight” of the place before it.
What are the values of the respective ”places” in the Mayan system?
Also, determine thevalues of these Mayan numbers:

?

?

?
3

?

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Question 4
Digital computers use a numeration system with a base of two, rather than a base of ten as we are
accustomed to using. It is much easier to engineer circuitry that counts in ”binary” than it is to design
circuits that count in any other base system. Based on what you know of numeration systems, answer the
followingquestions:
•
•
•
•

How many different symbols (ciphers) are there in the binary numeration system?
What are the different place-weight values in the binary system?
How would you represent the number ”seventeen” in binary?
In our base-ten (denary) numeration system, each character is called a ”digit.” What is each character
called in the binary numeration system?
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Question 5
Ifa digital meter display has four digits, it can represent any number from 0000 to 9999. This constitutes
ten thousand unique numbers representable by the display. How many unique numbers could be represented
by five digits? By six digits?
If an ancient Mayan ledger had spaces for writing numbers with three ”digits” each, how many unique
numbers could be represented in each space? What if thespaces were expanded to hold four ”digits” each?
If a digital circuit has four bits, how many unique binary numbers can it represent? If we expanded its
capabilities to eight bits, how many unique numbers could be represented by the circuit?
After answering these questions, do you see any mathematical pattern relating the number of ”places”
in a numeration system and the number of unique...