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.

128	6	32	16	8	4	2	1
0	0	0	0	0	0	0	0

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).

Hexadecimal to Denary:

4096	256	16	1
0	0	0	0

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.

4. Add the values

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).

Binary to Hexadecimal:

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.

-128	64	32	16	8	4	2	1
MSB							LSB

Negative denary number to binary Two’s Complement:

Find the binary equivalent of the denary number
Add an extra bit before the MSB and turn that into 0
Shift all 0 to 1 and 1 to 0
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 = 1001_BCD = 9₁₀
1000111₂ = 0100 0111_BCD = 47₁₀
10100111000.101₂ = 0101 0011 0001.1010_BCD = 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