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| | [[Category:Sound]] | | [[Category:Sound]] |
| | [[Category:Digital Theory]] | | [[Category:Digital Theory]] |
| − | ==Binary Math==
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| − | '''OPTIONAL'''
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| − | Binary Math
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| − | http://www.ibiblio.org/obp/electricCircuits/Digital/DIGI_2.html
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| − | What can one byte (8 bits) store?
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| − | 2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0
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| − | 1 1 1 1 1 1 1 1
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| − | 128 64 32 16 8 4 2 1
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| − | 128+64+32+16+8+4+2+1 = 255
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| − | What about negative numbers?
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| − | Signed Magnitude
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| − | Use the first bit as the equivalent of a +/- sign.
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| − | http://www.math.grin.edu/~rebelsky/Courses/152/97F/Readings/student-binary.html 510 in 8 bit binary
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| − | 00000101
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| − | -510 in 8 bit binary Signed Magnitude
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| − | 10000101
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| − | (make sure that the circuit knows you are using singed magnitude otherwise this could be interpreted as 113)
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| − | Now what can one byte (8 bits) store?
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| − | +/- 2^6 2^5 2^4 2^3 2^2 2^1 2^0
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| − | 0 1 1 1 1 1 1 1
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| − | + 64 32 16 8 4 2 1
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| − | 64+32+16+8+4+2+1 = 127
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| − | or
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| − | +/- 2^6 2^5 2^4 2^3 2^2 2^1 2^0
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| − | 1 1 1 1 1 1 1 1
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| − | - 64 32 16 8 4 2 1
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| − | -64+32+16+8+4+2+1 = -127
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| − | ===One's Compliment===
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| − | One's Compliment uses regular binary numbers to represent positive numbers. To make that number negative you just flip all the bits from 1 to 0 or 0 to 1.
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| − | 510 in 8 bit binary
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| − | 00000101
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| − | -510 in 8 bit binary One's Compliment
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| − | 11111010
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| − |
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| − | ===Two's Compliment===
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| − | Same as One's Compliment bit add one to negative numbers
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| − | 510 in 8 bit binary
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| − | 00000101
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| − | -510 in 8 bit binary Two's Compliment
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| − | 11111011
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| − | To figure out the sign of the answer we must check the MSB (most significant bit).If MSB is 0 number is positive, interpret normally If MSB is 1 number is negative
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| − |
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| − | * complement all bits
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| − | * add 1
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| − | * interpret as negative number
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