Number Systems and Conversions Quiz

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Questions and Answers

What is the equivalent of decimal 15 in hexadecimal?

F (correct)

Which number is represented as '1010' in decimal?

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?

13 Signup and view all the answers

What is the base of the hexadecimal number system?

16 Signup and view all the answers

What is the binary representation of the octal number 7058?

1110001012 Signup and view all the answers

How would you convert the decimal number 123410 to octal?

Divide by 8 and use the remainders. Signup and view all the answers

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

00010000101011112 Signup and view all the answers

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

In groups of three from right to left. Signup and view all the answers

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

2BB16 Signup and view all the answers

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

4D216 Signup and view all the answers

How would you convert an octal number directly to hexadecimal?

Use binary as an intermediary. Signup and view all the answers

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

Use binary as an intermediary. Signup and view all the answers

What is the decimal equivalent of the binary number 101011?

43 Signup and view all the answers

How do you convert the octal number 724 to decimal?

7 x 8^2 + 2 x 8^1 + 4 x 8^0 Signup and view all the answers

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

Divide by two and track remainders Signup and view all the answers

What is the hexadecimal equivalent of the decimal number 2748?

ABC Signup and view all the answers

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

The bit position starts from 0 on the right Signup and view all the answers

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

C x 16^0 + B x 16^1 + A x 16^2 Signup and view all the answers

What method is used when converting octal numbers to decimal?

Multiply each digit by 8^n Signup and view all the answers

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

The leftmost bit Signup and view all the answers

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

117 Signup and view all the answers

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

1048576 Signup and view all the answers

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

703 Signup and view all the answers

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

101110 Signup and view all the answers

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

41 Signup and view all the answers

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

0.000000000001 Signup and view all the answers

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

1001011 Signup and view all the answers

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

mega Signup and view all the answers

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

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Description

Test your knowledge of different number systems including decimal, binary, octal, and hexadecimal. This quiz covers the representation of numbers and the methods for converting between these systems. Challenge yourself with conversions and see how well you understand the structure of numbers.