Binary Numbers

What is a Binary Number?

A binary number is a number expressed in the binary (base 2) numeral system.
This number system uses only two digits – 1 and 0 – to represent all its values.
Digital computers use the binary number system due to its straightforward implementation in digital electronic circuitry using logic gates.
Each digit in a binary number is referred to as a bit.

Binary numbers are positional; the place value of each digit in a binary number is 2 raised to the power of its position, beginning with zero from the right.
As examples:
- The binary number 11 equals 3 in decimal (2^1 * 1 + 2^0 * 1).
- The binary number 101 equals 5 in decimal (2^2 * 1 + 2^1 * 0 + 2^0 * 1).

To convert a binary number to decimal, begin at the rightmost bit (least significant bit), multiply it by 2 to the power of its position, and continue to the left, summing up the products.
To convert a decimal number to binary, repeatedly divide by 2, recording the remainder at each step, until you reach zero. The binary number is the sequence of remainders, read in reverse order.
Practice is key to become proficient in these conversions.

Binary addition follows a similar process to decimal addition. Here’s how it works, from right to left:
- 0 + 0 = 0
- 1 + 0 = 1 (and vice versa)
- 1 + 1 = 0, with a carry of 1 to the next higher bit (similar to carrying in decimal addition)
- 1 + 1 + carry = 1, with a new carry of 1.
Binary subtraction requires understanding the concept of borrowing, much like in decimal subtraction:
- 1 - 0 = 1
- 0 - 1 = 1 with a borrow of 1 from the next higher bit
- 1 - 1 = 0
- 0 - 0 = 0
Again, mastery comes with practice.

Overall, a deep understanding of binary numbers is critical since they form the core of all processes in digital computers.