# Information Representation ## Information Representation

Number System

Binary: Abinary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically, “0” (zero) and “1” (one) where each digit is called a bit.

Binary to Denary:

1. Create a table with headings 128/64/32/16/8/4/2/1.

2. Insert the binary number into the table.

3. Add up all numbers that correspond with a 1.

Example

• 110011012 = 128 + 64 + 8 + 4 + 1 = 20510

Denary to Binary:

1. Create the same table.

2. Place 1s in the columns that add up to make the denary number.

3. Take the empty spaces as 0 and form a binary number.

Example

Suppose that you wanted to convert the denary number 21010 into binary

• The maximum place value that can go into 210 is 128, so you would set the digit that corresponds to 128 to 1.
• 210 − 128 = 82. The maximum place value that can go into 82 is 64, so you would set the digit that corresponds to 64 to 1.
• 82 − 64 = 18. The maximum place value that can go into 18 is 16, so you would set the digit that corresponds to 16 to 1.
• 2 – 2 = 0. The subtraction process ends. You would now set all remaining digits to 0.
• Therefore, 21010 = 110100102

Hexadecimal: The hexadecimal numeral system, often shortened to “hex”, is a numeral system made up of 16 symbols (base 16).

1. Create table with headings 4096/256/16/1 in the style shown above.

2. Put hex number in columns from right to left.

3. Multiply each hex digit with the corresponding column.

Example

Converting 2D to denary

• Separate the hex digits into 2 and D and find the equivalent binary numbers (2 = 0010; D = 1101).
• Piece them together to get 00101101 (0x128 + 0x64 + 1×32 + 0x16 + 1×8 + 1×4 + 0x2 + 1×1 = 45 in denary).

1. Split the binary number into three groups starting from the right.

2. Put each group into a table with 8/4/2/1 columns.

3. Add the columns that correspond with a 1 for each table.

4. Convert all the values into hex format and put them together.

Example

1×26+1×25+0x24+1×23+0x22+1×21+0x20= 64+32+0+8+0+2+0= (106)10Then, convert it into hexadecimal number= (106)10= 6×161+10×160= (6A)16 which is the answer.

Two’s Compliment: Two’s complement is the way most computers represent positive or negative integers.

Negative denary number to binary Two’s Complement:

1. Find the binary equivalent of the denary number
2. Add an extra bit before the MSB and turn that into 0
3. Shift all 0 to 1 and 1 to 0
4. Add 1 to the binary digit

Example

Find -4 using two’s complement numbers

• 4 = 100
• Adding 0 to the front becomes 0100
• ‘Inverted’ becomes 1011
• Add 1 = 1100 (-8 + 4 = -4)

BCD (binary coded decimal): It is a process for converting decimal numbers into their binary equivalents

Decimal to BCD:

1.  Separate the decimal number into its weighted digits

2.  Write down the equivalent 4-bit BCD code representing each decimal digit

Example

• 8510 = 1000 0101 (BCD)
• 57210 = 0101 0111 0010 (BCD)
• 857910 = 1000 0101 0111 1001 (BCD)

BCD to Decimal:

1.  Divide the binary number into groups of four digits, starting with the least significant digit

2. Write the decimal digit represented by each 4-bit group

3. Add additional zeros at the end if required to produce a complete 4-bit grouping

Example

• 10012 = 1001BCD = 910
• 10001112 = 0100 0111BCD = 4710
• 10100111000.1012 = 0101 0011 0001.1010BCD = 538.62510

Image Representation

Bitmap images: It is an image file format used to store digital images.

Vector graphic: A graphic consisting of components defined by geometrical formulae such as line, color and style

Picture Element (pixel): The smallest identifiable component of a bitmap image, defined by just two properties: its position in the bitmap matrix and its color

Image Resolution: The number of pixels an image contains per inch or per centimeter.

Screen resolution: The number of pixels per row by the number of pixels per column

File Size = Number of pixels  x  Color Depth

• The higher the color depth, the better color quality
• The higher the color depth, the larger the file size.

Sound

Analogue to Digital Converter: converts analogue sound into digital signals which can be stored digitally

Digital to Analogue Converter: converts digital signals into analogue sound

Sampling Rate: Number of samples taken per second

Sample resolution: The sampling resolution is the representation (or size of the numbers) used to write samples in digital sound recording

Higher the sample rate, bigger the file size

Bit rate: Number of bits required to store 1sec of sound

Bit Rate=Sampling Rate x Sampling Resolution

Video

Lossless compression: Coding techniques that allow subsequent decoding to recreate exactly the original file

Lossy compression: Coding techniques that cause some information to be lost so that the exact original file cannot be recovered in subsequent decoding

Frame Rate: Frequency at which frames in a video sequence are displayed on a screen

Higher the frame rate, better the video quality