Today’s computers use a binary symbol set
- Two symbol system to represent information in computers (primarily)
- Examples…
  - Heads/Tails
  - Modulo 2 Arithmetic
  - Statements that are True/False
  - 1/0
  - Yes/No
  - and so on
A Bit is a binary digit
- A bit $\in {0, 1}$
A Bit String - an ORDERED sequence of bits
- 1101 is a bit string, and is a different one from 1011
- 1 is a valid bit string (just a very short one)
A Byte - an 8 bit bit-string

Representing Bits Electrically

We use voltage on a wire to represent bits
Use 2 distinct voltage bands with a gap to reduce representation errors
We can represent a k-bit bit string using k wires, one per bit in the bit string.
- So if we wanted to represent a 128 bit bit-string, we would need 128 wires
Bus - a collection of k wires carrying the k bits of a k-bit bit string; $k \geq 1$
- Bus diagram may be k lines or a single line labeled with k or with k understood implicitly
- Basically a bus is a collection of wires to carry k bits of a bit string. On diagrams, we don’t necessarily draw all the wires we just imply how many wires are actually necessary

Bit Strings

Digital information is all compromised of bit strings
Bit strings can represent anything (as long as there’s enough storage)
- Because of this, computers are broadly useful
Bit strings by themselves have no meaning
- They gain meaning when paired with a representation
- Representation is a lens through which we view a meaning
- Pair a bit string with a different representation and you get a different meaning
- Representations
  - Integers Representation
  - Text Representation
  - Floating Point Representation
  - char, int, float, struct (the base data types)
  - Image, Text (complex data types made up of more data types)
A k-bit string is made of a sequence of k independent choices from {0, 1}
There are $2^{k}$ distinct k-bit strings (From the Product Rule of combinatorics)
k bits can
- be transported on just k wires
- yet can represent up to $2^{k}$ distinct values