Chapter 3 - Binary Numbering System CMIT100 Chapter 3 - Binary Numbering System

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.

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

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

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

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

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

Converting between Decimal and Binary

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

ASCII 7-bit 128 combinations

Extended ASCII 8-bit 256 combinations

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

Unicode Table (Example)

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

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

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

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

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

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

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

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

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

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

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

Integrated Circuits

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