Module 1.2: Data Representation

Data Representation

Refers to the form in which data is stored, processed, and transmitted.

Unique Code

A common way to represent text is to agree on a ________ for every symbol that needs to be presented.

8-bit

ASCII uses _____ strings to represent the English alphabet. 

Representing images

Images are also encoded using bit patterns.

Pixels

an image is divided into many small picture elements or also called as ______.

Binary Form

The appearance of each pixel is then encoded in _______.

Bitmap

The collection of these encoded pixels is known as the _______ of the image.

3 bytes

A color image usually uses _______ to represent a single pixel.

Graphic Interchange Format (GIF)

One such method that reduces the size of a bitmap file by reducing the number of colors that can be assigned to a pixel to 256.

256

Graphic Interchange Format (GIF) one such method that reduces the size of a bitmap file by reducing the number of colors that can be assigned to a pixel to ______.

Joint Photographic Experts Group (JPEG)

Developed a compression method which is commonly used to compress photographs.

Representing Numbers

Represent all numbers as binary numbers we can actually represent the numbers 0 to 127 with 8 bits.

Floating Point

The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point computation which was established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE).

Institute of Electrical and Electronics Engineers

IEEE

754 floating point

IEEE Standard ________ is the most common representation today for real numbers on computers, including Intel-based PC’s, Macs, and most Unix platforms.

The Sign of Mantissa
The Biased Exponent
The Normalized Mantissa

IEEE 754 has 3 basic components.

The Sign of Mantissa

This is as simple as the name. 0 represents a positive number while 1 represents a negative number.

The Biased Exponent

The exponent field needs to represent both positive and negative exponents. A bias is added to the actual exponent in order to get the stored exponent.

The Normalized Mantissa

The mantissa is part of a number in scientific notation or a floating-point number, consisting of its significant digits. Here we have only 2 digits.

32 bits

Single Precision IEE 754 Floating-Point Standard consists of ______ bits.

1 bit (31^st bit)

Single Precision IEE 754 Floating-Point Standard consists of ______ bit of signs.

8 bits

Single Precision IEE 754 Floating-Point Standard consists of ______ bits of exponent.

23 bits

Single Precision IEE 754 Floating-Point Standard consists of ______ bits of mantissa.

1 bit (63^rd bit)

Double Precision IEE 754 Floating-Point Standard consists of ______ bit of signs.

11 bits

Double Precision IEE 754 Floating-Point Standard consists of ______ bits of exponent.

52 bits

Double Precision IEE 754 Floating-Point Standard consists of ______ bits of mantissa.

Zero
Denormalized
Infinity
Not A Number (NAN)

IEEE has reserved some values that can ambiguity.

Zero

A special value denoted with an exponent and mantissa of 0. -0 and +0 are distinct values, though they both are equal.

Denormalized

If the exponent is all zeros, but the mantissa is not then the value is a _________ number. This means this number does not have an assumed leading one before the binary point.

Infinity

The values +infinity and -infinity are denoted with an exponent of all ones and a mantissa of all zeros. The sign bit distinguishes between negative infinity and positive infinity. Operations with infinite values are well defined in IEEE.

Not A Number (NAN)

Used to represent a value that is an error. This is represented when exponent field is all ones with a zero sign bit or a mantissa that it not 1 followed by zeros. This is a special value that might be used to denote a variable that doesn’t yet hold a value.