Digital Fundamentals Number Systems Quiz

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the hexadecimal representation of the binary number 1001 0110 0000 1110?

960F

9A0F

960E (correct)

9A0E

Which of the following is the decimal equivalent of the hexadecimal number 1A2F?

6695 (correct)

6795

6885

6555

What is the maximum hexadecimal digit?

F (correct)

Which of the following binary representations corresponds to the decimal number 13?

1101 Signup and view all the answers

What is the value of the hexadecimal digit 'C' in decimal?

12 Signup and view all the answers

When converting the binary number 0110 to hexadecimal, what is the result?

6 Signup and view all the answers

Which statement correctly defines the powers of 16 in the hexadecimal system?

They increase from right to left. Signup and view all the answers

How many unique values can be represented by a single hexadecimal digit?

16 Signup and view all the answers

What is the first step in converting the binary number 1 001 011 000 001 1102 to octal?

Group the binary number by 3-bits from the right Signup and view all the answers

What does the octal number system use as its base?

Base 8 Signup and view all the answers

What is the octal equivalent of the binary number 0110?

6 Signup and view all the answers

Which of the following correctly represents powers of 8 in the octal system?

1, 8, 64, 512 Signup and view all the answers

What is the decimal equivalent of the octal number 37028?

2458 Signup and view all the answers

How many digits are used in the octal number system?

8 Signup and view all the answers

In the octal system, which digit values are directly represented by the binary code 0000 to 0111?

0 to 7 Signup and view all the answers

What is the purpose of grouping binary numbers in sets of three when converting to octal?

To match octal digit values Signup and view all the answers

What characteristic distinguishes Gray code from binary code in applications such as shaft encoders?

Gray code changes only one bit at a time. Signup and view all the answers

What is the maximum number of characters that can be represented using standard 7-bit ASCII?

128 Signup and view all the answers

Which of the following methods can be used to detect a single-bit error in data transmission?

Parity Method Signup and view all the answers

How does the Hamming Code detect errors in data?

Through multiple parity bits at specific positions. Signup and view all the answers

Which of the following bits would you append to the ASCII character 'a' (1100001) to achieve even parity?

1 Signup and view all the answers

What is one function of extended ASCII compared to original ASCII?

It encodes 256 symbols instead of 128. Signup and view all the answers

What type of error detection method requires an additional bit to ensure a specific number of 1s?

Parity Method Signup and view all the answers

Why is Gray code preferable over binary for certain applications?

It minimizes the risk of errors during code transitions. Signup and view all the answers

What is the decimal equivalent of the binary number 100101.01?

37.25 Signup and view all the answers

Which method is used to convert a binary number to decimal?

Adding column values of bits that are 1 Signup and view all the answers

What is the binary representation of the decimal number 49?

110001 Signup and view all the answers

When converting a decimal fraction to binary, what is the next step after multiplying the fractional part by 2?

Record the whole number part Signup and view all the answers

What is the result of converting the decimal fraction 0.188 to binary up to five significant digits?

.00110 Signup and view all the answers

How do you convert a decimal number to another base?

Divide the decimal by the base repeatedly Signup and view all the answers

What is the incorrect assumption about converting binary to decimal?

Column weights are irrelevant Signup and view all the answers

What does the 'carry' denote when converting a decimal fraction to binary?

The binary place value Signup and view all the answers

What is the radix of the decimal number system?

10 Signup and view all the answers

Which of the following correctly represents the column weights of decimal numbers?

$10^5, 10^4, 10^3, 10^2, 10^1, 10^0$ Signup and view all the answers

How can the decimal number 480.52 be expressed in column value terms?

(4 x 10^2) + (8 x 10^1) + (0 x 10^0) + (5 x 10^{-1}) + (2 x 10^{-2}) Signup and view all the answers

Which of the following statements accurately describes binary numbers?

Binary has a radix of two and uses the digits 0 and 1. Signup and view all the answers

What is the column weight for the digit '1' in a binary number system?

$2^0$ Signup and view all the answers

Which of these expressions correctly forms the decimal number 9240 using column values?

(9 x 10^4) + (2 x 10^3) + (4 x 10^1) + (0 x 10^0) Signup and view all the answers

How does the placement of digits in a decimal number affect its value?

The value of each digit depends on its position in relation to the decimal point. Signup and view all the answers

What negative power corresponds to the third digit after the decimal in a decimal number?

$10^{-3}$ Signup and view all the answers

Study Notes

Decimal Numbers

Decimal number system has a base (radix) of ten, using digits 0 to 9.
Column weights for decimal numbers are powers of ten, increasing from right to left.
For fractional parts, weights use negative powers of ten, decreasing from left to right.
Example: The number 9240 can be expressed as (9 × 10³) + (2 × 10²) + (4 × 10¹) + (0 × 10⁰).

Binary Numbers

Binary number system has a base of two, utilizing only two symbols: 0 and 1.
Column weights in binary are powers of two, expanding similarly from right to left.

Binary Conversions

To convert binary to decimal, sum the column values of the bits that are 1.
Example: 100101.01 converts to decimal as follows: 32 + 4 + 1 + 0.25 = 37.25.
Decimal whole numbers are converted to binary by representing each column weight until exceeding the target number.
Example: Decimal number 49 converts to binary as 110001.

Converting Decimal Fractions to Binary

For decimal fractions, repeatedly multiply the fraction by 2, recording carries.
Example: 0.188 converts to binary by successively calculating 0.188 × 2 and noting carries, giving .00110.

Conversion to Other Bases

Decimal can be converted to any base by repeatedly dividing by that base.
Example: Binary 1001 0110 0000 1110 converts to hexadecimal as 960E.

Hexadecimal Numbers

Hexadecimal system is base 16, with column weights as powers of 16.
Example: To convert 1A2F₁₆ to decimal, evaluate the weighted sum of each hexadecimal digit.

Octal Numbers

Octal system has a base of 8, where column weights are powers of 8.
Example: Converting 3702₈ to decimal involves summing the weighted values of each octal digit.

Gray Code

Gray code is a binary numeral system where only one bit changes between successive numbers, reducing errors in applications like shaft encoders.

ASCII Code

ASCII encodes alphanumeric and control characters, initially using 7 bits for 128 characters.
Extended ASCII introduced in 1981 increased the character set to 256 using 8 bits.
Unicode has been developed to represent characters from various languages beyond English.

Error Detection Codes

Three methods to detect single-bit errors:
- Parity Method
- Cyclic Redundancy Check (CRC)
- Hamming Code
The parity method adds an extra bit to ensure the total number of 1’s is either odd or even.
Example: The ASCII code for "a" (1100001) has an even number of 1's; thus, a parity bit of 0 is needed for odd parity.

Studying That Suits You

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

Description

Test your knowledge on number systems and operations based on the concepts presented in 'Digital Fundamentals'. This quiz covers various aspects of decimal numbers, their properties, and their applications in digital systems.