Process of Numeric Data Representation in the Computer

Numeric data are represented in the computer using straight binary coding, which encodes an entire number as a whole. Straight binary coding requires that numbers be stored in computer memories as a fixed number of bits.

A group of bits so treated as a unit is called a word, and the number of bits is called the length of the word. Let’s know the process of numeric data representation on the computer.

Numeric data representation

Integer Representation

Integers or fixed-point numbers have no decimal points. An integer 1 is represented in the memory of the computer by its binary form if 1 is positive, and by its 2’s complement if I am negative.

Example: Storing 1101001112 that is 42310, and – 42310 in 32-bit memory location

For simplicity, we assume that the word length is 32. The computer stores 423 which is 1101001112 in a 32-bit memory location by introducing 0s at the beginning of the binary form. Thus:

numeric data representation

The computer stores 423 in a memory location in 2’s complement form for 423, that is

numeric data representation

In the first display the dots represent omitted 0s; in the second omitted 1’s.

The computer can tell whether an integer 1 in memory is positive or negative by looking at the leftmost bit. If the leftmost bit is 0, then 1 is positive; if the leftmost bit is 1, then 1 is negative.

Accordingly, the largest (positive) integer that can be stored in a 32-bit memory location is

Numeric data representation
Numeric data representation

Or 2³¹ -1, which is approximately 2 billion. Similarly, the smallest (that is negative) integer that can be stored in a 32-bit memory location is -2³¹ -1, or approximately -2 billion.

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