L.O: STUDENTS WILL BE ABLE TO EXPLAIN HOW COMPUTERS USE HEX.

30-60 minutes (about 1 class period)

DO NOW: READ

Unit 4 Lab 1: Number Representation, Page 4

Using Hex:

THIS SUITCASE IS BINARY

THIS SUITCASE IS HEX

We can pack four bits (binary digits) into one hexadecimal

digit because 16 is a power of two (16 = 24).

So, a group of four bits represents a value between 0 and 15, and one hex digit also represents values from 0-15

(using 0-9 and A-F). This makes it easier to translate

between binary and hex than between other bases.

Translating between Binary and Hex

• To translate a binary numeral (like 11010111012) to hexadecimal, start by splitting it into groups of four bits, from right-to-left (like this: 11 0101 1101)

• Then determine the value of each group and write the corresponding hex digit (look it up on the table at right)

BINARY HEX

00002 016

00012 116

00102 216

00112 316

01002 416

01012 516

01102 616

01112 716

10002 816

10012 916

10102 A16

10112 B16

11002 C16

11012 D16

11102 E16

You can create a table like this whenever you need one

EX: 112 = 316, 01012 = 516, and 1101 = D16.

So, 11010111012=35D16

.

FOR YOU TO DO:Translate these binary numerals to

hexadecimal notation:

1.1110112

2.11011112

3.101100012

BINARY HEX

00002 016

00012 116

00102 216

00112 316

01002 416

01012 516

01102 616

01112 716

10002 816

10012 916

10102 A16

10112 B16

11002 C16

11012 D16

11102 E16

Translating Hex TO BINARY

• To translate a HEX numeral (like

4E116) to Binary, write each hex digit as a group of four bits, ( write that way even if the binary representation doesn’t need all four digits)

• For ex: 416 = 01002, E16 = 11102, and 1 = 00012.

BINARY HEX

00002 016

00012 116

00102 216

00112 316

01002 416

01012 516

01102 616

01112 716

10002 816

10012 916

10102 A16

10112 B16

11002 C16

11012 D16

11102 E16

You can create a table like this whenever you need one

4E116 =0100111000012 or just 100111000012

Translate these hexadecimal numerals to

binary notation:

a. 1816

b. 5D16

c. F816

Remember: practice makes perfect.On the AP exam, you’ll have to translate binary to hex and vice

versa!

Hexadecimal ColorsHow do you think a computer knows what color to make an

object?

Computers have several ways of representing colors: RGB (red, green, blue)

CMYK (cyan, magenta, yellow, black)….

RGB (red, green, blue) is used for screen displays,They use CMYK (cyan, magenta, yellow, black) is used for

printing…

On a computer screen, each pixel—each dot that makes up the picture on the screen—is assigned an

RGB color defined by the intensity of red, green, and blue in that color.

The three color intensities each range from 0 to 255 (one byte is used for each of the three

colors), which is 00 to FF in hex notation.

If (R, G, B) = (128, 0, 255), the color is purple: some red and a lot of blue, but no

green at all.

If all three colors are as bright as possible (all are 255), we see whiteif they are as dark as possible

(0,0,0), we see black.

Instead of writing (255, 255, 255) for white and (128, 0, 255) for purple, we often use hex notation: FFFFFF and 8000FF. And this color is red 255, green 127, and blue 0, which is

FF7F00 in hex.

Represent these colors in hex notation:

a.red 0, green 149, and blue 235

b.red 128, green 90, and blue 0

c. red 163, green 0, and blue 84

a.red 0, green 149, and blue 235 is 0095EB in hex

b.red 128, green 90, and blue 0 is 805A00 in hex

c.red 163, green 0, and blue 84 is A30054 in hex

•Predict what this RGB color will look like based on its values: red 145, green 0, blue 226.

•Predict what this hex RGB color will look like: 04FF61.

If There Is Time…

• Explore this RGB/HEX color converter: http://hex.colorrrs.com/

• Play with this Interactive Color Wheel

• Read more about RGB colors and hexadecimal notation.

Take It Further (Extension Activities)

A. Load the Snap! RGB library into one of your projects to explore RGB color further. In the File menu, choose "Libraries..." and then choose "Set RGB or HSV pen color". This will give you a new "Pen" block:

As in all Snap! blocks, the numeric input slots take values in base 10 (not hex). Each color

component has a value between 0 and 255

Learning Objectives:

• LO 2.1.1 Describe the variety of abstractions used to represent data. [P3]

• LO 2.1.2 Explain how binary sequences are used to represent digital data. [P5]

Enduring Understandings:

•EU 2.1 A variety of abstractions built upon binary sequences can be used to represent all digital data.

Essential Knowledge:

1. EK 2.1.1A Digital data is represented by abstractions at different levels.

2. EK 2.1.1B At the lowest level, all digital data are represented by bits.

3. EK 2.1.1C At a higher level, bits are grouped to represent abstractions, including but not limited to numbers, characters, and color.

4. EK 2.1.1D Number bases, including binary, decimal, and hexadecimal, are used to represent and investigate digital data

Essential Knowledge:

• 5. EK 2.1.1E At one of the lowest levels of abstraction, digital data is represented in binary (base 2) using only combinations of the digits zero and one.

• 6. EK 2.1.1F Hexadecimal (base 16) is used to represent digital data because hexadecimal representation uses fewer digits than binary.

• 7. EK 2.1.1G Numbers can be converted from any base to any other base.

• 8. EK 2.1.2A A finite representation is used to model the infinite mathematical concept of a number.

Essential Knowledge:

• 9. EK 2.1.2B In many programming languages, the fixed number of bits used to represent characters or integers limits the range of integer values and mathematical operations; this limitation can result in overflow or other errors.

• 10.EK 2.1.2C In many programming languages, the fixed number of bits used to represent real numbers (as floating point numbers) limits the range of floating point values and mathematical operations; this limitation can result in round off and other errors.

Essential Knowledge:

• 11. EK 2.1.2D The interpretation of a binary sequence depends on how it is used.

• 12. EK 2.1.2E A sequence of bits may represent instructions or data.

• 13. EK 2.1.2F A sequence of bits may represent different types of data in different contexts.

• 14. EK 6.2.2J The bandwidth of a system is a measure of bit rate—the amount of data (measured in bits) that can be sent in a fixed amount of time.

• 15. EK 6.2.2K The latency of a system is the time elapsed between the transmission and the receipt of a request.