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Number Representation

Explore the fundamentals of number representation in digital signal processing, including how decimal numbers convert to binary and the differences among sign magnitude, ones complement, and two's complement formats. Understand why two's complement is widely used for arithmetic operations in digital machines.

We have learned that the field of digital signal processing manipulates sequences of numbers. In a digital machine, these numbers can only be represented in a binary format. In the case of fixed-point arithmetic, there is a set procedure that converts a decimal number (e.g., a voltage or current signal) into its binary representation for positive numbers. For example, the number 1313 can be written as:

13=1×101+3×100=10+313 = 1\times 10^1 + 3\times 10^0=10+3 ...