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# Binary Slides

## on Jul 31, 2010

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• 2 “Computers process information by the way they use electricity.  The number one is represented by the electricity being switched on and zero is represented by the electricity being switched off (A Binary Primer).”
• 2 Explain the decimal numbers we use today (ones, tens, hundreds, thousands, etc.). Show the relation between place value and powers of 10.
• 3 5. Expanded form examples: Show the number 2,538. Briefly explain the place value of each digit. Point to different digits in the number 6,947 and ask students to name the value of the digit. Show the way that we carry place value from ones to tens when adding.
• 3 “Computers process complex information by encoding it in a system of ones and zeros, called binary. The binary number system uses only ones and zeros (Binary Primer).” Explain the base-two place values, or powers of two. “Each cell contains a binary digit (bits).” Show table from library and ask what patterns are noticed (odd numbers, even numbers, twos place, fours place, etc.).
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• 4 Demonstrate converting 010010 and 0011010from binary to decimal.
• 3 Demonstrate converting 11 and 28 from decimal to binary.
• 7 Practice: Introduce Excel sheet. Ask students how to convert 17 and 24. Show sum and explain how base-two systems carry to the next place.
• 6 Using the binary handout, have students work with a partner for 5 minutes to convert between decimal and binary numbers. Quickly review answers, allowing students time to correct mistakes as needed.
• 3Binary Multipliers: Review chart and relate to internal and external memory.
• 5 Windows Calculator: Demonstrate how to use the Windows Calculator to convert numbers between binary and decimal.
• 1“In conclusion, bits are binary digits. Each bit can hold the value 0 or 1. Bytes are made up of 8 bits each. Binary math works just like decimal math, but each bit can have a value of only 0 or 1. Microchips use transistors to process the information (on and off electrical currents) so the computer understands it.”
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## Binary Slides Presentation Transcript

• Johnna Noles
Ecomp7100
Binary Number System
• What do computers do?
• Having a good understanding of how binary works is fundamental to knowing many other aspects of how all digital technology works, including computers, networks, PDAs, cell telephones, TVs, etc.
Rationale
Objective: to realize the importance of the binary number system and convert numbers between base-ten and base-two number systems.
• Processing Information
Electricity is either on or off.
1=on
0=off
• Decimal Numbers
Base-Ten System
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
95
96
97
98
99
100
101
15
16
17
18
19
20
21
22
23
24
Thousands
Hundreds
Tens
Ones
103
102
101
100
10-1
10-2
Decimal Point
• Expanded Form
Thousands
Hundreds
Tens
Ones
103
102
101
100
10-1
10-2
2 5 3 8
6 9 4 7
2000+500+30+8=2538
6000+900+40+7=6947
• Binary Numbers
Base-Two System
0
1
10
11
100
101
111
1000
1001
1010
1011
1100
1101
1110
1111
10000
110
Sixteens
Eights
Fours
Twos
Ones
24
23
22
21
20
16
8
4
2
1
Value
• Binary Numbers, Simplified
“Binary Numbers in 60 Seconds”
• Converting: Binary to Decimal
24
23
22
21
20
4
2
1
8
16
1
0
0
0
1
(16x1)+(8x0)+(4x0)+(2x1)+(1x0) =
18
1
0
1
0
1
(16x1)+(8x1)+(4x0)+(2x1)+(1x0) =
25
• Converting: Decimal to Binary
24
23
22
21
20
4
2
1
8
16
11 =
1
1
1
0
0
28 =
0
1
0
1
1
17 + 24 = ____
• Partner Work
Assignment: With a partner, you have 5 minutes to convert decimal numbers to binary numbers.
1
1
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
• Bits and Bytes
• Easy Conversions
• Summary
Bits are binary digits.
Each bit can hold the value 0 or 1. Bytes are made up of 8 bits each.
Binary math works just like decimal math, but each bit can have a value of only 0 or 1.
Microchips use transistors to process the information (on and off electrical currents) so the computer understands it.
• “There are only 10 kinds of people in this world, those who understand binary and those who don’t.”
• References