Define the following computer Fundamental of binary arithmetic?

Binary arithmetic is a fundamental concept in computer science, particularly in the representation and manipulation of data using binary digits (bits), which have values of 0 and 1. Here's how the basic arithmetic operations are defined in binary arithmetic:

Binary Addition:

Binary addition is the process of adding two binary numbers together, similar to how decimal numbers are added. In binary addition, each bit position is treated separately, and a carry can occur when the sum of two bits at the same position is 2 or more.

Here's an example of binary addition:

1101 (13 in decimal)

+ 1010 (10 in decimal)

--------

10111 (23 in decimal)

Binary Subtraction:

Binary subtraction is the process of subtracting one binary number from another, similar to decimal subtraction. Like in binary addition, each bit position is treated separately, and a "borrow" can occur when subtracting a larger bit value from a smaller one.

Here's an example of binary subtraction:

1101 (13 in decimal)

- 101 ( 5 in decimal)

--------

100 ( 8 in decimal)

Binary Multiplication:



Binary multiplication is the process of multiplying two binary numbers together, similar to decimal multiplication. It involves shifting and adding the partial products obtained from multiplying individual bits.

Here's an example of binary multiplication:

1101 (13 in decimal)

× 101 ( 5 in decimal)

-----------

1101 (Partial product, shifted by 0 positions)

0000 (Partial product, shifted by 1 position)

1101 (Partial product, shifted by 2 positions)

-----------

100001 (65 in decimal)

In binary arithmetic, the principles of place value and carrying over (for addition) and borrowing (for subtraction) still apply, but the carry and borrow values are typically 2 rather than 10, as in decimal arithmetic. Multiplication involves bit-by-bit multiplication and shifting, followed by adding the partial products.

Understanding binary arithmetic is essential for computer systems because digital data is stored and processed using binary representation. Computer hardware components use binary logic gates to perform these arithmetic operations at a very basic level, enabling complex calculations and operations in computer programs.