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+ | Hello World! lol | ||
+ | |||
+ | |||
+ | =====Number Systems Conversions===== | ||
+ | |||
+ | A selection of different problems for your solving pleasure. Be sure to focus on the process, not just the answer. | ||
+ | |||
+ | =====Powers of 2===== | ||
+ | |||
+ | ^ Exponent | ||
+ | | 2e0 | 1 | | ||
+ | | 2e1 | 2 | | ||
+ | | 2e2 | 4 | | ||
+ | | 2e3 | 8 | | ||
+ | | 2e4 | 16 | | ||
+ | | 2e5 | 32 | | ||
+ | | 2e6 | 64 | | ||
+ | | 2e7 | 128 | | ||
+ | | 2e8 | 256 | | ||
+ | | 2e9 | 512 | | ||
+ | | 2e10 | 1024 | | ||
+ | | 2e11 | 2048 | | ||
+ | | 2e12 | 4096 | | ||
+ | | 2e13 | 8192 | | ||
+ | | 2e14 | 16384 | | ||
+ | | 2e15 | 32768 | | ||
+ | | 2e16 | 65536 | | ||
+ | | 2e17 | 131072 | ||
+ | | 2e18 | 262144 | ||
+ | | 2e19 | 524288 | ||
+ | | 2e20 | 1048576 | ||
+ | |||
+ | =====Powers of 8===== | ||
+ | |||
+ | ^ Exponent | ||
+ | | 8e0 | 1 | | ||
+ | | 8e1 | 8 | | ||
+ | | 8e2 | 64 | | ||
+ | | 8e3 | 512 | | ||
+ | | 8e4 | 4096 | | ||
+ | | 8e5 | 32768 | | ||
+ | | 8e6 | 262144 | ||
+ | | 8e7 | 2097152 | ||
+ | | 8e8 | 16777216 | ||
+ | | 8e9 | 134217728 | ||
+ | | 8e10 | 1073741824 | ||
+ | | 8e11 | 8589934592 | ||
+ | |||
+ | =====Powers of 16===== | ||
+ | |||
+ | ^ Exponent | ||
+ | | 16e0 | 1 | | ||
+ | | 16e1 | 16 | | ||
+ | | 16e2 | 256 | | ||
+ | | 16e3 | 4096 | | ||
+ | | 16e4 | 65536 | | ||
+ | | 16e5 | 1048576 | ||
+ | | 16e6 | 16777216 | ||
+ | | 16e7 | 268435456 | ||
+ | |||
+ | =====Conversions between Powers of 2===== | ||
+ | |||
+ | ^ Binary Number | ||
+ | | 0101011101 | ||
+ | | 000111010101100 | ||
+ | | 11011110101011 | ||
+ | | 00110100010111111011 | ||
+ | | 000101100101010001010 | ||
+ | | 11111110110111000110010101000011 | ||
+ | |||
+ | =====Conversions involving Base 10===== | ||
+ | |||
+ | ^ Binary Number | ||
+ | | 11011011000 | ||
+ | | 111111111 | ||
+ | | 1000000000 | ||
+ | | 000111111111111 | ||
+ | | 000001000000000000000000 | ||
+ | | 000110101101011101 | ||
+ | | ? | ? | 1000 | ? | | ||
+ | | ? | ? | 7168 | ? | | ||
+ | | ? | ? | 16383 | ? | | ||
+ | | 0001000000000000 | ||
+ | | 1111111111111111 | ||
+ | | 0101101001011010 | ||
+ | |||
+ | =====Challenge===== | ||
+ | Not required, but a good test of concepts. | ||
+ | |||
+ | ^ Exponent | ||
+ | | 7e0 | 1 | | ||
+ | | 7e1 | 7 | | ||
+ | | 7e2 | 49 | | ||
+ | | 7e3 | 343 | | ||
+ | | 7e4 | 2401 | | ||
+ | | 7e5 | 16807 | | ||
+ | |||
+ | ^ Binary Number | ||
+ | | ? | 1234 | ? | ? | ? | | ||
+ | | ? | 6144 | ? | ? | ? | | ||
+ | |||
+ | |||
+ | < | ||
+ | |||
+ | For anyone who was confused by the lesson on " | ||
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+ | </ | ||
+ | |||
+ | Let's use the example of the Octal value 24. Why is Octal 24 equal to the number 20 in our typical "base 10" lives? Because equivalent values existing in the < | ||
+ | |||
+ | Now lets try switching bases, but preserving the < | ||
+ | |||
+ | Here's an Example:< | ||
+ | |||
+ | When dealing with the digit 94< | ||
+ | |||
+ | Understanding this, we should be able to recognize that once we reach 99, and need to continue, we will be able to roll one of the imaginary leading zeros up to our next digit and reset everything that follows.< | ||
+ | |||
+ | Counting upward in Base 10:< | ||
+ | 000094< | ||
+ | 000095< | ||
+ | 000096< | ||
+ | 000097< | ||
+ | 000098< | ||
+ | 000099< | ||
+ | 000100 - We simply call this 100, and typically ignore the laws behind why it's a 1 followed by two 0's (The same< | ||
+ | 000101 & | ||
+ | 000102< | ||
+ | |||
+ | We're going to increase the value of our column to the left by 1 factor each time we reach our maximum in the column to it's right. If we apply this concept while counting in any base then we should be able to list the numbers of any number system consecutively. Becoming familiar is simply a matter of practice. | ||
+ | </ | ||