One of the greatest stumbling blocks for me in my academic life has been a major distaste for the numerical voodoo we know as math, so as I now have a fragile grip on some crucial concepts I am going to express my understanding in written form for posterity and as an aid to any fellow geeks.

**Binary To Decimal**

- Create a table of the first 8 powers of 2 like so starting at zero and write your binary number from right to left in the row below
- For each digit (bit) where the value is one add together the power value above the number in the table
- The result of this addition is the binary number expressed in decimal (base 10)

**Example:**

Lets convert 11011000_{2 }to decimal:

First we create the power table:

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |

1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 |

Next we add the powers of the bits which are not zero giving us the equivalent base 2 (decimal) number

128 + 64 + 16 + 8 = 216_{10}

Questions: *Q:* *What is the meaning of the subscript numbers after the binary and decima*l digits?

**A**: These indicate what base applies to a given number a 2 means the number is base 2 (binary) and a 10 means the number is base 10 (decimal)

*Q: Why do we use powers of two for binary:*

**A:** Because binary is base 2 meaning that place values increase by a power of two for each place.

*Q: Why do we use the first eight powers:*

**A:** Because binary numbers get long quickly we generally only work with numbers that can fit into one byte (8 bits) meaning that the binary numbers we work with will be a maximum of eight digits, hence the use of the first eight powers

*Q: Why do all powers of zero equal 1:*

**A:** This is still a mystery to me. my teacher says it’s a rule and it seams to work so I’d stick with it.

Decimal to binary will be covered in the forthcoming part 2

Bleh. Maths is just pooey. It only raped my brain until 5th form. From then on I’ve only used simple maths. Much easier that way.