Binary%20Numbers?

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Binary Numbers?

• Foley
• SED 514 Section 1.14

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How do numbers work?

• Counting
• 0 1 2 3 4 5 6 7 8 9 10
• 10
• Why isnt there a symbol for 10?

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Decimal Number

• What is the value of 123?
• 3 ones (100)
• 2 tens (101)
• 1 hundreds (102)
• (1 x 100) (2 x 10) (3 x 1)

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What if we only had 8 fingers?

• We would not have the numbers 8 9
• We would count up to 7 and then 10!
• Why?
• What would 100 be?

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Octal Numbers

• What is the value of 123base8?
• 3 ones (80)
• 2 eights (81)
• 1 sixty-fours (82)
• What is that in decimal?
• (1 x 64) (2 x 8) (3 x 1)

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What if you only had 2 fingers?

• Only two digits 0 and 1
• What is the value of 123base2?

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Numbers in binary

• OK, what is the value of 111base2?
• 1 ones (20)
• 1 two (21)
• 1 four (22)
• What is that in decimal?
• (1 x 4) (1 x 2) (1 x 1)

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More questions
Binary Decimal
101
10001
1010101
123
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Why do we care about binary?

• Key to computers - all you need are 1s and 0s
• Just like a light switch, on 1 off 0
• Hard part, making a circuit that could change
  itself - so you could add
• Vacuum tubes and then transistors and finally
  integrated circuits