Decimal & Binary Conversions For The Hopeless: Part 1

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

  1. 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
  2. For each digit (bit) where the value is one add together the power value above the number in the table
  3. The result of this addition is the binary number expressed in decimal (base 10)

Example:

Lets convert 110110002 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 = 21610

Questions:
Q: What is the meaning of the subscript numbers after the binary and decimal 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

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One thought on “Decimal & Binary Conversions For The Hopeless: Part 1

  1. 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.

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