Number Systems and Conversions Quiz

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson
Download our mobile app to listen on the go
Get App

Questions and Answers

What is the equivalent of decimal 15 in hexadecimal?

  • C
  • E
  • D
  • F (correct)

Which number is represented as '1010' in decimal?

  • 14
  • 12
  • 8
  • 10 (correct)

In which number system is the symbol '1' used exclusively?

  • Decimal
  • Octal
  • Binary (correct)
  • Hexadecimal

Which of the following numbers is represented as '1101' in decimal?

<p>13 (A)</p> Signup and view all the answers

What is the base of the hexadecimal number system?

<p>16 (C)</p> Signup and view all the answers

What is the binary representation of the octal number 7058?

<p>1110001012 (D)</p> Signup and view all the answers

How would you convert the decimal number 123410 to octal?

<p>Divide by 8 and use the remainders. (B)</p> Signup and view all the answers

What is the binary representation for the hexadecimal number 10AF16?

<p>00010000101011112 (B)</p> Signup and view all the answers

To convert from binary to octal, how do you group the bits?

<p>In groups of three from right to left. (A)</p> Signup and view all the answers

Which of the following correctly converts the binary number 10101110112 to hexadecimal?

<p>2BB16 (A)</p> Signup and view all the answers

What is the output when converting the decimal number 123410 to hexadecimal?

<p>4D216 (C)</p> Signup and view all the answers

How would you convert an octal number directly to hexadecimal?

<p>Use binary as an intermediary. (A)</p> Signup and view all the answers

When converting the hexadecimal number 1F0C16 to octal, which method is used?

<p>Use binary as an intermediary. (B)</p> Signup and view all the answers

What is the decimal equivalent of the binary number 101011?

<p>43 (B)</p> Signup and view all the answers

How do you convert the octal number 724 to decimal?

<p>7 x 8^2 + 2 x 8^1 + 4 x 8^0 (B)</p> Signup and view all the answers

What is the first step in converting a decimal number to binary?

<p>Divide by two and track remainders (B)</p> Signup and view all the answers

What is the hexadecimal equivalent of the decimal number 2748?

<p>ABC (D)</p> Signup and view all the answers

Which of the following correctly describes the position of the bits when converting binary to decimal?

<p>The bit position starts from 0 on the right (D)</p> Signup and view all the answers

To convert the hexadecimal number ABC to decimal, which calculations should be performed?

<p>C x 16^0 + B x 16^1 + A x 16^2 (B)</p> Signup and view all the answers

What method is used when converting octal numbers to decimal?

<p>Multiply each digit by 8^n (D)</p> Signup and view all the answers

When converting a binary number like 1100 to decimal, which bit contributes to the highest value?

<p>The leftmost bit (C)</p> Signup and view all the answers

What is the decimal equivalent of the binary number '1110101'?

<p>117 (B)</p> Signup and view all the answers

In computing, what is the value of the prefix 'M' in base 2?

<p>1048576 (A)</p> Signup and view all the answers

Which of the following correctly lists the decimal equivalent of the hexadecimal number '1AF'?

<p>703 (B)</p> Signup and view all the answers

What is the result of adding the binary numbers '10101' and '11001'?

<p>101110 (A)</p> Signup and view all the answers

What is the equivalent octal representation of the decimal number 33?

<p>41 (A)</p> Signup and view all the answers

What does the prefix 'p' represent in the metric system?

<p>0.000000000001 (D)</p> Signup and view all the answers

Which of the following is the correct binary representation of the decimal number 75?

<p>1001011 (A), 1001011 (C)</p> Signup and view all the answers

In the context of common powers, what is 10^6 commonly known as?

<p>mega (C)</p> Signup and view all the answers

Flashcards

Decimal Number System

A number system with base 10, using the symbols 0-9.

Binary Number System

A number system with base 2, using the symbols 0 and 1.

Octal Number System

A number system with base 8, using the symbols 0-7.

Hexadecimal Number System

A number system with base 16, using the symbols 0-9 and A-F.

Signup and view all the flashcards

Decimal to Binary Conversion

Repeated division by 2, noting the remainders, which are then read in reverse order.

Signup and view all the flashcards

Binary to Decimal Conversion

Multiply each bit by 2^n, where n is the bit position (from right starting at 0).

Signup and view all the flashcards

Decimal to Octal Conversion

Repeated division by 8, tracking the remainders.

Signup and view all the flashcards

Octal to Decimal Conversion

Multiply each digit by 8^n, where n is the digit's position (from right starting at 0).

Signup and view all the flashcards

Decimal to Hexadecimal Conversion

Repeated division by 16, noting the remainders (0-9, A-F).

Signup and view all the flashcards

Hexadecimal to Decimal Conversion

Multiply each digit by 16^n, where n is the digit's position (from right starting at 0).

Signup and view all the flashcards

Binary to Octal Conversion

Group binary digits into sets of three (starting from the right) and convert each group to its octal equivalent.

Signup and view all the flashcards

Binary to Hexadecimal Conversion

Group binary digits into sets of four (starting from the right) and convert each group to its hexadecimal equivalent.

Signup and view all the flashcards

Octal to Binary Conversion

Convert each octal digit to its 3-bit binary representation.

Signup and view all the flashcards

Hexadecimal to Binary Conversion

Convert each hexadecimal digit to its 4-bit binary representation.

Signup and view all the flashcards

Hexadecimal to Octal Conversion

Convert to binary first, then group the binary into threes and convert to octal.

Signup and view all the flashcards

Octal to Hexadecimal Conversion

Convert to binary first, then group the binary into fours and convert to hexadecimal.

Signup and view all the flashcards

pico (p)

10^(-12)

Signup and view all the flashcards

nano (n)

10^(-9)

Signup and view all the flashcards

micro (µ)

10^(-6)

Signup and view all the flashcards

milli (m)

10^(-3)

Signup and view all the flashcards

kilo (k)

10^(3)

Signup and view all the flashcards

mega (M)

10^(6)

Signup and view all the flashcards

giga (G)

10^(9)

Signup and view all the flashcards

tera (T)

10^(12)

Signup and view all the flashcards

kilo (k) in Base 2

2^10 = 1024

Signup and view all the flashcards

mega (M) in Base 2

2^20 = 1,048,576

Signup and view all the flashcards

giga (G) in Base 2

2^30 = 1,073,741,824

Signup and view all the flashcards

Binary 1-Bit Addition

Basic rules for adding single bits in binary.

Signup and view all the flashcards

Binary n-Bit Addition

Add bits column by column, carrying over when the sum is 2 or more.

Signup and view all the flashcards

Study Notes

Number Systems

  • Common number systems: decimal, binary, octal, hexadecimal
  • Decimal: base 10, uses symbols 0-9
  • Binary: base 2, uses symbols 0 and 1, used in computers
  • Octal: base 8, uses symbols 0-7
  • Hexadecimal: base 16, uses symbols 0-9 and A-F

Quantities and Counting

  • Numbers can be represented in different number systems
  • Example: The decimal number 10 is equal to 1010 in binary, 12 in octal and A in hexadecimal

Conversion Between Number Systems

  • Decimal to Decimal: Just for fun, no conversion needed
  • Decimal to Binary: Divide by 2 repeatedly, keep track of remainders
  • Decimal to Octal: Divide by 8 repeatedly, keep track of remainders
  • Decimal to Hexadecimal: Divide by 16 repeatedly, keep track of remainders
  • Binary to Decimal: Multiply each bit by 2^n, where n is the bit position starting from 0 on the right
  • Octal to Decimal: Multiply each bit by 8^n, where n is the bit position starting from 0 on the right
  • Hexadecimal to Decimal: Multiply each bit by 16^n, where n is the bit position starting from 0 on the right
  • Binary to Octal: Group bits in threes, starting from the right, convert to octal digits
  • Binary to Hexadecimal: Group bits in fours, starting from the right, convert to hexadecimal digits
  • Octal to Binary: Convert each octal digit to a 3-bit binary representation
  • Hexadecimal to Binary: Convert each hexadecimal digit to a 4-bit binary representation
  • Octal to Hexadecimal: Use binary as an intermediary
  • Hexadecimal to Octal: Use binary as an intermediary

Common Powers

  • Base 10:
    • pico (p) = 10^-12
    • nano (n) = 10^-9
    • micro (µ) = 10^-6
    • milli (m) = 10^-3
    • kilo (k) = 10^3
    • mega (M) = 10^6
    • giga (G) = 10^9
    • tera (T) = 10^12
  • Base 2: (used in computing, particularly for memory)
    • kilo (k) = 2^10 = 1024
    • mega (M) = 2^20 = 1,048,576
    • giga (G) = 2^30 = 1,073,741,824

Binary Addition

  • Adding two 1-bit values:
    • 0 + 0 = 0
    • 0 + 1 = 1
    • 1 + 0 = 1
    • 1 + 1 = 10 (carry over the "1")
  • Adding two n-bit values:
    • Add individual bits
    • Propagate carries

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

Related Documents

Numbering Systems - Module 3.1 PDF

More Like This

Conversion of Number Systems Quiz
10 questions

Conversion of Number Systems Quiz

UserFriendlyHarpsichord avatar
UserFriendlyHarpsichord
Number Systems Basics
10 questions

Number Systems Basics

ImprovingCrocus avatar
ImprovingCrocus
Binary to Decimal Number Conversion
6 questions

Binary to Decimal Number Conversion

StylizedTsilaisite2673 avatar
StylizedTsilaisite2673
Binary to Decimal Number Conversion
5 questions

Binary to Decimal Number Conversion

StylizedTsilaisite2673 avatar
StylizedTsilaisite2673
Use Quizgecko on...
Browser
Open
Browser
Browser