Number Systems and Conversions Quiz

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Questions and Answers

What is the most significant bit (MSB) in a binary number?

The bit representing the median value

The rightmost bit

The leftmost bit (correct)

The bit representing the smallest value

Which of the following hexadecimal values is equivalent to the binary value 1111?

F (correct)

What is the denary equivalent of the binary number 101010?

42 (correct)

When converting a denary number to binary, what is the correct method to use?

Sucessively divide by 2 and record the remainders from bottom to top (A) Signup and view all the answers

What must be done with the binary value before converting it into hexadecimal?

Divide the bits into groups of 4 (C) Signup and view all the answers

Which of the following represents the value 15 in hexadecimal?

F (A) Signup and view all the answers

How do you convert hexadecimal value '1A' into binary?

00011010 (B) Signup and view all the answers

What is the binary value of denary number 29?

11101 (B) Signup and view all the answers

What effect does increasing the sampling resolution have on sound quality?

Increases accuracy of the sampled sound (D) Signup and view all the answers

Which of the following correctly describes image resolution?

Number of pixels that make up an image (A) Signup and view all the answers

How is the file size of a mono sound file calculated?

Sample rate × sample resolution × length of sample (B) Signup and view all the answers

What does 'colour depth' refer to in bitmap images?

Number of bits representing each colour (D) Signup and view all the answers

What type of compression does the MP3 file format utilize?

Lossy compression (A) Signup and view all the answers

What does 'bit depth' increase when referring to sound?

The accuracy of the sampled sound wave (B) Signup and view all the answers

What is a key feature of MIDI files?

They consist of a series of commands without actual sound (A) Signup and view all the answers

What are bitmap images made up of?

Pixels (D) Signup and view all the answers

Which format is used primarily for compressing photographic images?

JPEG (C) Signup and view all the answers

What does RLE stand for in file compression?

Run-Length Encoding (B) Signup and view all the answers

Which of the following represents a condition under which RLE is efficient?

Long strings of repeated values (D) Signup and view all the answers

What is the main disadvantage of using a higher sampling rate?

Increased memory usage (C) Signup and view all the answers

What does the colour depth of 8 bits allow for in terms of colours?

256 colours (C) Signup and view all the answers

What is the hexadecimal representation of the values 2, 1, 15, and 13 combined?

21FD (C) Signup and view all the answers

During binary addition, what is the result of adding binary values 1 and 1?

1 with a carry of 1 (A) Signup and view all the answers

What occurs when the sum from a binary addition exceeds the maximum number of bits allowed?

Overflow (A) Signup and view all the answers

What is the two's complement of the binary value 1101100?

0010100 (B) Signup and view all the answers

How is hexadecimal commonly utilized in programming?

For defining colors in HTML (B) Signup and view all the answers

What is the range of values represented by an 8-bit two's complement?

-128 to 127 (C) Signup and view all the answers

Which of the following statements correctly describes binary addition?

1 + 0 = 1 (B) Signup and view all the answers

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

Locate the highest binary place value (C) Signup and view all the answers

Which of the following is a correct statement regarding shift operations?

Shifting left doubles the binary value. (A) Signup and view all the answers

What is the binary equivalent of the decimal value 13?

1101 (A) Signup and view all the answers

What is the ASCII value of the string character 'A'?

65 (D) Signup and view all the answers

Which method is used for representing negative binary values?

Two's Complement (A) Signup and view all the answers

Which of the following best describes how binary and denary values differ?

Binary is represented in bits, while denary uses digits (A) Signup and view all the answers

In the context of logical shifts, what happens to the bits of the binary number?

They shift and fill in with 0s (B) Signup and view all the answers

Study Notes

Number Systems

Binary: Base-2 system. Uses only 0 and 1 (representing OFF and ON). MSB is the leftmost bit.
Denary: Base-10 system. Uses values 0-9.
Hexadecimal (Hex): Base-16 system. Uses 0-9 and A-F (A=10, B=11, ..., F=15).

Number Conversions

Binary to Denary: Assign powers of 2 to each bit position (from right to left, starting with 2⁰). Add the values where the binary digit is 1.
Denary to Binary: Repeatedly divide by 2, recording the remainders. Read the remainders from bottom to top to get the binary equivalent.
Hexadecimal to Binary: Separate each hex digit, convert to denary, then convert each denary value to binary. Combine the binary values.
Binary to Hexadecimal: Divide the binary string into groups of 4 bits (from right to left), add leading zeros if necessary. Convert each group to its hexadecimal equivalent.
Hexadecimal to Denary: Convert the hexadecimal value to binary, then convert the binary value to denary following the power of 2 method.
Denary to Hexadecimal: Convert the denary value to binary, then convert the binary value to hexadecimal as described above.

Binary Calculations

Addition: Binary addition follows specific rules: 0+0=0, 1+0=1, 0+1=1, 1+1=0 (carry 1), 1+1+1=1 (carry 1).
Overflow: Occurs when the result of an operation exceeds the number of bits available to store it.

Logical Shifts

Left Shift: Shifts each bit to the left by a specified number of positions. Empty positions are filled with 0s.
Right Shift: Shifts each bit to the right by a specified number of positions. Empty positions are filled with 0s.

Two's Complement

Representing Negative Values: Used to represent negative values in binary. The most significant bit (MSB) is treated as the sign (1 for negative, 0 for positive). The magnitude of the negative number is calculated following the above denary to binary conversion rules.
Conversion: To convert a negative binary value to two's complement, first find the binary equivalent of the value (ignoring the -). Invert all bits, then add 1 to the result. To convert a two's complement value to denary, follow the denary to binary conversion process.

Applications of Hexadecimal

Defining Colors (HTML): Representing colors in web design.
MAC Addresses: Unique identifiers for network devices.
Assembly Language/Machine Code: Used in low-level programming.
Memory Dumps: Displaying the contents of computer memory.
Error Codes: Representing memory locations of errors.
IP Addresses: Used to identify devices on the Internet.

Text, Sound, and Images

ASCII: 7-bit character set, representing letters, numbers, and symbols.
Unicode: Character set capable of representing many international languages using up to 4 bytes per character.
Sound: Analog sound converted to digital through sampling.
- Sampling Resolution (Bit Depth): Number of bits to represent each sample. Larger resolutions lead to more accurate sound but increased file size.
- Sampling Rate: Number of samples taken per second (measured in Hertz). Higher rates lead to higher sound quality.
Bitmap Images: Images made of pixels.
- Color Depth: Number of bits per pixel, determining the number of colors the image can display. Higher depths increase file size.
- Image Resolution: Number of pixels in the image, more pixels give more detail. Lower resolution images are 'pixelated'.
File Size Calculation:
- Images: Resolution × Color depth
- Sound: Sampling rate × Sample resolution × Length (in seconds)
File Types:
- MIDI: Stores music data as commands; no actual audio is stored initially. Uses serial transmission.
- MP3: Lossy format for audio compression, often reducing file size by up to 90%.
- MP4: Multi-media file container format.
- JPEG: Lossy format for image compression, reducing the original resolution.
File Compression:
- Lossless: Does not reduce quality, reconstructs the original file perfectly. Examples include Run-Length Encoding (RLE) for repeated data.
- Lossy: Reduces file size by discarding data; quality is lost. Examples include MP3 and JPEG.

Memory Measurement

Bit: Binary digit.
Byte: 8 bits.
Kilobyte (KB), Megabyte (MB), Gigabyte (GB), Terabyte (TB): Units of memory, based on powers of 1000 (Conventional System).
Kibibyte (KiB), Mebibyte (MiB), Gibibyte (GiB), Tebibyte (TiB) ...: Units of memory, based on powers of 1024 (IECB System). This system is increasingly standard for accurate representation, especially in computing.

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Description

Test your understanding of different number systems including binary, denary, and hexadecimal. This quiz covers key concepts and conversion methods between these systems. Challenge yourself with various questions that reinforce your knowledge of number systems.