1. Chapter 3 - Binary Numbering System
CMIT100
Chapter 3 - Binary Numbering System

2. Learning Objectives
Describe Numbering Systems: decimal, binary, octal, and hexadecimal.
Describe how characters are stored in computer memory.
Demonstrate the application of binary (Boolean) operations of AND, OR, NOT, and XOR on binary numbers.
Illustrate the use of binary in a computer with a focus on IP addresses.

3. Numbering Systems Decimal – Base 10 Binary – Base 2 Octal – Base 8
Hexadecimal – Base 16

4. Base 10 System - Decimal Primary human numbering system Digits 0 – 9
Example: 1, 2, 10, 4,321

5. Base 2 System - Binary Native numbering system for digital computers
Two digits: 0, 1
Each digit is a bit that represents on or off
Eight bits is a byte; also known as an octet
Example: 0, 1, 10, 101, 1100

6. Base 8 - Octal
Digits 0 – 7
Examples: 1, 5, 112

7. Base 16 - Hexadecimal
Digits 0 – F
Examples: 0, 1, 3FA7

8. Converting between Decimal and Binary

9. Character Representation
American Standard Code for Information Interchange (ASCII)
Unicode – An extension of ASCII
EBCDIC - Discontinued

10. ASCII
7-bit
128 combinations

11. Extended ASCII
8-bit
256 combinations

12. Unicode Extended ASCII is not enough for international use
One Unicode mapping uses 16 bits per character
65363 Combinations
Unicode is a superset of ASCII
The first 256 characters correspond exactly to the extended ASCII character set

13. Unicode Table (Example)

14. Binary Operations NOT AND OR NAND NOR XOR
Gate - A device that performs a basic operation on electrical signals
Circuit - Gates combined to perform more complicated tasks

15. Binary Operations – NOT
A NOT gate accepts one input signal (0 or 1) and returns the opposite signal as output

16. Binary Operations – AND
An AND gate accepts two input signals
If both are 1, the output is 1; otherwise, the output is 0

17. Binary Operations – OR An OR gate accepts two input signals
If both are 0, the output is 0; otherwise, the output is 1

18. Binary Operations – NAND
The NAND gate accepts two input signals
If both are 1, the output is 0; otherwise, the output is 1

19. Binary Operations – NOR
The NOR gate accepts two input signals
If both are 0, the output is 1; otherwise, the output is 0

20. Binary Operations – XOR
An XOR gate accepts two input signals
If both are the same, the output is 0; otherwise, the output is 1

21. Review of Gate Processing
A NOT gate inverts its single input
An AND gate produces 1 if both input values are 1
An OR gate produces 0 if both input values are 0
An XOR gate produces 0 if input values are the same
A NAND gate produces 0 if both inputs are 1
A NOR gate produces a 1 if both inputs are 0

22. Constructing Gates A transistor has three terminals A source A base
An emitter, typically connected to a ground wire

23. Constructing Gates
The easiest gates to create are the NOT, NAND, and NOR gates

24. Combinational Circuits
Gates are combined into circuits by using the output of one gate as the input for another

25. Integrated Circuits

26. Creative Commons Statement