**The Binary Number System**

*Binary sequences *** **— sequences of 0’s and 1’s — are used to represent all computer data.

- Numbers
- Letters and text.
- Images.
- Machine language instructions.
- Sounds and video.
- Every kind of data you find on a computer.

*Binary system *is similar to the decimal system.

- Both are
*positional number systems.*- 542 is 500 + 40 + 2.

**Decimal is a base-10 system:**

- 10 digits, 0 through 9

- Place values are powers of 10: 1’s, 10’s, 100’s, 1000’s, etc.
- Each place is previous place times 10
- Both are
*positional number systems.*- 101 is 4 + 0 + 1 = 5

**Binary is a base-2 system:**

- 2 digits, 0 through 1
- Place values are powers of 2
- 1s, 2s, 4s, 8s, 16s, etc.
- Each place is previous place times 2

**Hardware Abstraction Layers:** Binary data is processed by physical layers of hardware

**Physical electronic circuits:** At the lowest level, physicists and electrical engineers develop materials and design and build electronic circuits that are composed of *transistors*, the fundamental building block of electronic devices.

**Gates and flip flops:** Computer scientists and electrical engineers combine basic circuits into basic computational elements, such as AND gates and S/R flip flops.

**Integrated Circuits (ICs):** Electrical and computer engineers combine low-level elements into complex integrated circuits or computer chips.

**Abstraction:** A general representation of something.

**1. Figure out what decimal value is represented by the following binary number 0011 1010 0011**

= 931

**2. Represent the decimal value 517 as a binary number.**

= 1000000101

**3. The binary number system is base 2 and has 2 digits. The decimal number system is base 10 and has 10 digits. The octal system is base 8. How many digits does it have? What are they, starting at 0?**

The octal system has 8 digits: 0,1,2,3,4,5,6,7

**4. Suppose the number 523 is a base-8 octal number. What would its value be in decimal? In binary?**

The octal value 523 is 339 in decimal. In binary it would be 1000001011.

## Comments by Cara Bradley