1. Binary Numbers?
Foley
SED 514 Section 1.14
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2. Why isn’t there a symbol for 10?
How do numbers work?
Counting
10?
Why isn’t there a symbol for 10?
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4. 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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6. 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 “10” be equal to?
What would “100” be?
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7. Octal Numbers What is the value of 123:base8? 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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8. What if you only had 2 fingers?
Only two digits 0 and 1
What is the value of 123:base2?
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9. Numbers in binary OK, what is the value of 111:base2? 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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10. More questions
Binary
Decimal
101
10001
123
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11. Why do we care about binary?
Just like a light switch, on = 1 off =0
We can count (and remember) with electricity!
Vacuum tubes and then transistors and finally integrated circuits
Key to computers - all you need are 1s and 0s
Give a number to all letters and you can do anything (ASCII)
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