Converting from Binary to Denary and Binary Addition

Converting Binary to Denary

Binary is a base-2 system used in computing due to its simplicity of having only two possible states: 1 (on) and 0 (off).
A denary system, also known as the decimal system, is more commonly used in our daily lives, it is a base-10 system.
While converting a binary number to a denary number, start from the right-most digit (also known as the least significant bit or LSB) and move towards the left.
Each successive digit signifies an increasing power of 2, starting with 2^0 for the LSB.
Multiply each binary digit by its corresponding power of 2 and sum these products. The total value is the denary equivalent of the binary number.

Binary addition is performed similarly to typical addition, with rules adapted for base-2 values.
For 0 + 0, the result is 0.
For 0 + 1 or 1 + 0, the result is 1.
For 1 + 1, the result is 10 (2 in denary), with 1 carrying over to the next column.
A carry occurs when adding two ‘1’s, similar to how a carry works in denary addition. The ‘1’ carries forward and is added to the sum calculated in the next column.
For situations where there is a carry from a previous calculation, such as 1 (carry) + 1 + 0, the result is 10, with 1 carrying over to the next column.
For calculations with a carry such as 1 (carry) + 1 + 1, the result is 11, with 1 carrying over to the next column.
The sum is read from left to right, the reverse of the order in which the calculation was performed.