Binary Numbers? Foley SED 514 Section 1.14 1/2/2019

Why isn’t there a symbol for 10? How do numbers work? Counting 0 1 2 3 4 5 6 7 8 9 10 10? Why isn’t there a symbol for 10? 1/2/2019

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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) 1/2/2019

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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 “10” be equal to? What would “100” be? 1/2/2019

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) 1/2/2019

What if you only had 2 fingers? Only two digits 0 and 1 What is the value of 123:base2? 1/2/2019

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) 1/2/2019

More questions Binary Decimal 101 10001 1010101 123 1/2/2019

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) 1/2/2019