Counting, Conversion & Koans Bits, Bits, Bits Counting, Conversion & Koans

Counting in Binary

Binary Binary can encode any number that decimal numbers can We use the place a number occurs to determine its value For example, 12345 1 is in the 104 place 2 is in the 103 place 3 is in the 102 place 4 is in the 101 place 5 is in the 100 place

Binary Binary is also place value numbered Take the binary number 1000100 1 is in the 26 place 0 is in the 25 place 0 is in the 24 place 0 is in the 23 place 1 is in the 22 place 0 is in the 21 place 0 is in the 20 place

Counting When we count, as soon as we run out of digits in the current place, we go back to 0 (advancing the next place as well) 00 01 02 03 04 05 06 07 08 09 10

Counting Same in binary, there are just less numbers so you have to advance places more often 000 001 010 011 100 101 110 111

Conversion

Converting from Binary to Decimal We leverage the place value use system For example, with the number 0110110101 0 x 29 + 1 x 28 + 1 x 27 + 0 x 26 + 1 x 25 + 1 x 24 + 3 x 22 + 1 x 22 + 0 x 21 + 1 x 21 01101101012 = 43710 This trick actually works for any base to decimal (just change the base) For example, in ternary (0,1,2) 012012 0 x 35 + 1 x 34 + 2 x 33 + 0 x 32 + 1 x 31 + 2 x 30 0120123 = 14010

Converting from Decimal to Binary If multiplication let’s us convert the other way, it probably makes sense we use division to go backwards Repeatedly divide the number by the base you’re going to and keep the remainders. Stop when the quotient (answer of the division) is 0 140 to binary 140 / 2 = 70 r 0 70 / 2 = 35 r 0 35 / 2 = 17 r 1 17 / 2 = 8 r 1 8 / 2 = 4 r 0 4 / 2 = 2 r 0 2 / 2 = 1 r 0 1 / 2 = 0 r 1 Take the remainders in reverse so 14010 = 100011002

Other Bases If you want to convert from base 3 to base 9 Convert the base 3 number to base 10 Then convert the base 10 number to base 9

Koans of Bits

Koan? A “koan” is a paradoxical anecdote or riddle These koans of bits are over simplified

The Koans Of Bits It's all just bits. Perfect is normal. All data inside a computer or on the Internet is represented in binary 1’s and 0’s. It only appears that the computer has photos, songs, movies, documents, fonts, files, folders. The laws governing the handling of bits are tricky since many were written when there were distinct differences between radio waves and phone lines. Now a phone call and a web page are both bits. Perfect is normal. Duplication is identical. The idea of the “original” copy is meaningless.

The Koans Of Bits There is want in the midst of plenty. Some data is not digital and not accessible. Some data is the wrong format. Some data is impossible to find buried by other more visible data (search engines). Processing is power. Modern computers perform a trillion operations a second. Fast processing power has enabled impressive advances in AI and robot automation. Moore's Law—the density of integrated circuits doubles every few years. The prediction was made in 1965 and lasted 40 years.

The Koans Of Bits More of the same can be a whole new thing. Exponential change starts slowly, and many do not notice it in time. Examples: the switch to digital cameras; the death of the mall with online shopping Nothing goes away. Disk capacity has also followed Moore's law. We have the capacity to store everything, and government requires it for many businesses. Stores, hotels, schools track your activities. The capabilities result in even more being stored. For example, birth certificates include much more private information about the parents than before. Opportunities for research and mischief abound.

The Koans Of Bits Bits move faster than thought. Tasks can be outsourced all over the world without delays (e.g., call centers, drive through orders, radiologists, etc.). Being physically close to someone does not mean you receive information from them faster. Moving things around on the Internet has difficult legal problems, based on the laws of each country. A man in Switzerland was convicted of defamation for “liking” Facebook posts.