Numbers in Binary

Numbers in Binary

We're used to seeing numbers represented in base 10 "decimal" notation, but we can represent numbers in any base we please. In base 10 we use 10 symbols 0,1,2,3,...,9 and in base n we use n symbols 0,1,2,3,...,(n-1)

The simplest base is 2, because in that base we have only two symbols 0,1

Base 2 is also call "binary" and writing numbers in base 2 makes them look like computer data.

In binary the positions represent 1,2,4,8,16,32,.. so for example, the number 11 in binary is 1101, and this simply means..

11=(1)*1+(1)*2+(0)*4+(1)*8

Here's the first 20 prime numbers in binary..

2 01
3 11
5 101
7 111
11 1101
13 1011
17 10001
19 11001
23 11101
29 10111
31 11111
37 101001
41 100101
43 110101
47 111101
53 101011
59 110111
61 101111
67 1100001
71 1110001

Here's pi in binary..

pi=11.00100100 00111111 01101010 10001000 10000101 10100011 00001000 11010011 00010011 00011001 10001010 00101110 00000011 01110000 01110011 01000100 10100100 00001001 00111000 00100010 00101001 10011111 00110001 11010000 00001000 00101110 11111010 10011000 11101100 01001110 01101100 10001001 01000101 00101000 00100001 11100110 00111000 11010000 00010011 01110111 10111110 01010100 01100110 11001111 00110100 11101001 00001100 01101100 11000000 10101100 00101001 10110111 11001001 01111100 01010000 11011101 00111111 10000100 11010101 10110101 10110101 01000111 00001001 00010111 10010010 00010110 11010101 11011001 10001001 01111001 11111011 00011011 11010001 00110001 00001011 10100110 10011000 11011111 10110101 10101100 00101111 11111101 01110010 11011011 11010000 00011010 11011111 10110111 10111000 11100001 10101111 11101101 01101010 00100110 01111110 10010110..

What is this data stream encoding? Nobody knows.

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Content written and posted by Ken Abbott abbottsystems@gmail.com