SOP and POS Forms

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Unformatted text preview: SOP and POS Forms Password_________________ © Copyright 2009 Daniel Tylavsky ✔ Counting in Decimal(Base 10:Symbol 0- 9): ✔ 0+1=1 1+1=2 2+1=3 . . . 09 + 01 1 Carry 1 19 + 01 1 Carry 2 ✔ Counting in Binary (Base 2: Symbols 0-1): 01 + 01 1 Carry 1 00 + 01 1 SOP and POS Forms ✔ Carrying on in the same way. . . Decim al Binary 1 1 2 1 3 1 1 Decim al Binary 1 1 2 1 3 1 1 4 1 5 1 1 6 1 1 7 1 1 1 SOP and POS Forms ✔ To extend this to 4 variables, ABCD, we recognize that each variable carries a weight: – A B C D 2 3 2 2 2 1 2 8 4 2 1 ✔ Starting always with 0 count: – D (LSB) alternates between 0 and 1 at each count increment because its weight is 2 =1. – C alternates between 0 and 1 every other count increment because it’s weight is 2 1 =2. – How do B and A behave? SOP and POS Forms 4-Bit Binary Count Sequence Decimal Number A B C D 1 1 2 1 3 1 1 4 1 5 1 1 6 1 1 7 1 1 1 8 1 9 1 1 10 1 1 11 1 1 1 12 1 1 13 1 1 1 14 1 1 1 15 1 1 1 1 Note: Largest decimal number using n(4)-bits is:...
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