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6 positions, each 0-F value gives 6^16 options, yes?
by damir 2y ago
6 positions, each 0-F value gives 6^16 options, yes?
- nojvek 2y agoNot really. When numbers repeat, the value is the same. E.g 00 is the same as 00. So the possible outcomes is 6^16, but unique values per color channel is only 256 values. So unique colors are 256^3 = 16.7M colors.
- damir 2y agoYes, each possible 6^16 outcome is it's own subpage... /000000 /000001 /000002 /000003 etc... Or am I missing something?
- basic_ 2y agoyou mean 16^6
- elpocko 2y ago16^6 == 256^3 == 2^24 == 16,777,216
- kelnos 2y agoYou have it backward. There are 16^6 URLs, not 6^16.
- mkl 2y agoYou are missing something. How many two-digit decimal numbers are there from 00 to 99? Obviously 99+1 = 100: 10 options for the first digit times 10 options for the second digit; 10 in the form 0X, 10 in the form 1X, etc. up to 9X, a total of 10 * 10 = 10^2. So how many 6-digit hexadecimal numbers from 0x000000 to 0xffffff? 0xffffff+1 = 16777216 = 16^6. 16 options for the first digit, times 16 options for the second digit, times 16 for the 3rd, times 16 for the 4th, times 16 for the 5th, times 16 for the 6th is 16^6. Or go to bytes: 3 bytes, each with 256 possible values is 256^3 = (16^2)^3 = 16^6. Or bits: 2^24 = (2^4)^6 = 16^6. It's also pretty trivial to just count them. Run this in your browser console: count = 0; for(i = 0x000000; i <= 0xffffff; i++) { count++; } console.log(count, 16**6, 0xffffff+1, 6**16)
- Y_Y 2y ago256^3 == (16^2)^3 == 16^(3*2) == 16^6
- nojvek 2y agoYes. 16^6 is not 6^16.
- tromp 2y agoIf you think 3 positions, each 0-1, gives 3^2 options, then please show us the 9th three-bit number. Even simpler is the case of 1 position that is 0-1. Does that give 1^2 or 2^1 options?
- 123yawaworht456 2y ago1 byte (8 bits) is 2^8 (256 unique combinations of bits) 3 bytes (24 bits) is 2^24 (16777216 unique combinations of bits)
- ColinWright 2y agoYou have 6 hex characters. The first has 16 possible values; The second also has 16 possible values for each of those 16, so now we have 16 times 16. etc. So it's a choice from 16, repeated for a total of 6 times. That's 16 times 16 times ... times 16, which is 16^6.
- albedoa 2y agoWelp, you got me scrolling your HN thread to see where the "two-trillion-something" number came from. Between this and your experiment site, you have a knack for drawing attention.