the fundamentals of data representation

Describe the concept of bases in the context of Denary, Binary, and Hexadecimal.

Describe the concept of bases in the context of Denary, Binary, and Hexadecimal.

Bases refer to the number of different digits or combination of digits used in a number system. Denary uses 10 digits (0-9), Binary uses 2 digits (0, 1), and Hexadecimal uses 16 digits (0-9, A-F).

Define a bit and a nibble in the context of units of information.

A bit is the smallest unit of data in computing, representing a binary digit (0 or 1). A nibble consists of 4 bits.

How is a byte related to bits and nibbles?

A byte consists of 8 bits or 2 nibbles.

Do you know the sequence of units in increasing order from bit to petabyte?

Bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte, petabyte.

Describe the process of converting Denary to Binary.

List binary place values, place a one under the largest fitting value, subtract and repeat until the number becomes 0. The ones below the values represent the binary equivalent.

Explain the significance of binary in computer science.

Computers use binary because they operate using switches that can be either on (1) or off (0), making it a fundamental system for digital electronics.

How is the value of a binary number calculated from its digits?

Multiply each digit by the corresponding power of 2 based on its position, then sum the results to get the denary equivalent.

Define Kilobyte, Megabyte, Gigabyte, and Terabyte in terms of bytes.

Kilobyte = 1000 bytes, Megabyte = 1000 kilobytes, Gigabyte = 1000 megabytes, Terabyte = 1000 gigabytes.

Describe the process of converting binary to hexadecimal.

Group binary digits into nibbles of 4, convert each nibble to denary, then convert denary to hexadecimal using the conversion table, and finally combine the hex digits.

How do you convert a hexadecimal number to binary?

Split the hex number into individual values, convert each hex value to decimal, then convert each decimal to binary, and finally combine all digits to form one binary number.

Define binary shifts in multiplication and division.

In binary, shifting all digits to the left multiplies the number by 2^(number of places), while shifting to the right divides by 2^(number of places).

Do a binary addition example using the provided table.

Performing binary addition involves adding two binary digits along with any carry from the previous addition, following the rules outlined in the table.

How does shifting in binary multiplication work?

To multiply a binary number, shift all its digits to the left and fill gaps with 0s. For example, to multiply by 4, shift all digits two places to the left.

Explain the impact of losing a '1' during binary shifting.

Losing a '1' during shifting in binary multiplication/division can lead to incorrect or inaccurate results, affecting the final value.

Describe the process of converting denary to hexadecimal.

Convert denary numbers to binary, group binary digits into nibbles of 4, then convert each nibble to denary, and finally convert denary to hexadecimal using the conversion table.

How can binary shifting be used for division?

In binary division, shifting all digits to the right divides the number by 2^(number of places), providing a simple method for division operations.

Explain the concept of nibbles in binary conversion.

Nibbles are groups of 4 binary digits used when converting binary to hexadecimal, simplifying the conversion process by breaking down the binary number into manageable parts.

Do a binary multiplication example using shifting.

Perform a binary multiplication by shifting all digits to the left, multiplying the number by 2^(number of places) as per the shifting rules in binary operations.

Describe ASCII character encoding

ASCII is a character encoding standard that uses 8-bit characters to represent 128 characters, including control codes, punctuation, uppercase and lowercase letters, and numeric digits.

Define Unicode character encoding

Unicode is a character encoding standard that uses 16-bit or 32-bit characters to represent a much larger number of characters, including emojis, and shares the same codes as ASCII up to 127.

How are character codes in ASCII grouped?

Character codes in ASCII are grouped and run in sequence, where each character has a specific numerical value, making it possible to determine the values for other characters based on this sequence.

What is a pixel in image representation?

A pixel is the smallest unit in an image, defined by a color and represented in binary, with each pixel having a specific position.

Describe bitmapped images

Bitmapped images are composed of pixels, where each pixel is represented by a unique binary number corresponding to a color, arranged in a two-dimensional matrix to form the image.

Define colour depth in image representation

Colour depth refers to the number of bits used to represent a pixel, determining the range of colors that can be displayed in an image.

How is the number of colors in an image calculated based on colour depth?

The number of colors in an image is calculated as 2 raised to the power of the number of bits used for the color depth of each pixel.

What is the formula for calculating image file size in bits?

Image file size (in bits) = width in pixels × height in pixels × color depth in bits.

Describe sound representation

Sound is analog and does not follow the digital binary representation like images or characters.

Describe the process of converting analogue signals to digital form for storage and processing by a computer.

Analogue signals are sampled to digitalize sound, where a sample represents a measure of amplitude at a specific point in time. This process involves determining the sampling rate (number of samples per second in hertz) and the sample resolution (number of bits per sample). The size of a sound file in bits can be calculated by multiplying the sampling rate, sampling resolution, and the length of the sound in seconds.

Explain the concept of compression and differentiate between lossy and lossless compression methods.

Compression is a technique used to reduce file size. Lossy compression involves removing some data to make the file smaller, typically removing data that is least likely to be noticed. The original file cannot be fully restored from the compressed version. In contrast, lossless compression retains all information by identifying patterns in the data, allowing repeated data items to be stored once with instructions on how to restore them. The original file can be completely restored in lossless compression.

What are the reasons for compressing files?

File compression reduces size, enabling faster transmission, requiring less bandwidth, and lowering the cost of cloud storage.

Define Huffman coding and explain how it achieves lossless compression.

Huffman coding utilizes a binary tree to assign binary codes to data elements, like characters. It reduces the binary code length for longer data elements, placing them higher in the tree. Typically, right-hand paths are represented by 1 and left-hand paths by 0. This method achieves lossless compression by identifying patterns in the data and assigning shorter binary codes to frequently occurring elements.

How is the number of bits calculated for a phrase using a Huffman binary tree?

To calculate the number of bits for a phrase using a Huffman binary tree, one must refer to the tree structure to determine the binary code length for each character. By following the tree, the total number of bits needed for the phrase can be calculated based on the assigned binary codes for each character.

Describe how to calculate the number of bits for a phrase before compression using ASCII.

Count the number of characters in the phrase, including spaces, and multiply this number by 7.

Do in Run Length Encoding (RLE), how is data compressed?

RLE compresses data by specifying the number of times a character or pixel repeats, followed by the value of the character or pixel.

Define Run Length Encoding (RLE) in the context of data compression.

RLE is a lossless compression technique that represents data by indicating the repetition count of a character or pixel followed by the character or pixel value.

How can you calculate the total number of bits needed for a character in a phrase in the context of compression?

Multiply the number of bits by the frequency of the character to get the total number of bits needed for that character in the whole phrase.

Describe the process of calculating the total number of bits for the entire phrase in the context of compression.

Add together the total number of bits needed for each character in the phrase to determine the number of bits for the entire phrase.