Overview
This lecture explains what binary is, why computers use it, and how binary allows computers to represent numbers, text, and more.
Counting Systems Overview
- Tally marks are the simplest counting system; each mark equals one item.
- Base-10 positional system uses digits 0-9, adding a digit to the left for each power of ten.
- Each added base-10 digit increases the system's capacity by a power of ten.
How Binary Works
- Binary is a positional counting system using only two digits: 0 and 1.
- Each binary digit represents an increasing power of two (1, 2, 4, 8, etc.).
- Counting in binary is less efficient than base-10 but much better than tally marks.
Why Computers Use Binary
- Computers use micro transistors as tiny switches that are either ON (1) or OFF (0).
- Representing numbers with binary is more efficient than with tally marks in computers.
- One transistor equals one bit, which can be ON (1) or OFF (0).
Bits, Bytes, and ASCII
- A bit (binary digit) is the smallest unit, representing either 1 or 0.
- A byte is eight bits, representing numbers from 0 to 255.
- ASCII (American Standard Code for Information Interchange) assigns each character a number from 0 to 255.
- For example, uppercase 'A' is 65 in ASCII, which is 01000001 in binary.
Expansion to Larger Numbers
- To represent more than 255, computers can use two bytes (16 bits), increasing range up to 65,535.
- 8-bit means computers process 8 bits at a time; 16-bit means 16 bits at a time.
- More bits allow computers to represent larger numbers and more complex data.
Key Terms & Definitions
- Binary — A counting system using only 0 and 1, with each digit representing a power of two.
- Transistor — A tiny switch in a computer that can be ON (1) or OFF (0).
- Bit — Short for binary digit; the smallest unit of data in a computer.
- Byte — A group of 8 bits.
- ASCII — A code that assigns numbers to letters and symbols for computers to process text.
Action Items / Next Steps
- Review how numbers convert between base-10 and binary.
- Read about ASCII codes and practice converting characters to binary and vice versa.