Download PDF by A.P. Bowran: A Boolean Algebra: Abstract and Concrete

By A.P. Bowran

ISBN-10: 0333031164

ISBN-13: 9780333031162

ISBN-10: 134900216X

ISBN-13: 9781349002160

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I) and a current will flow along the wire if A = 1, but not if A = 0. ) The meanings of U and n are also similar to those met in previous chapters, for we say that (An B) represents ----A An B; B---A and Bin series Fig. (ii) where the current passes through A and B, and A and B are in series. Similarly, (A U B) represents (A u B); A or B; A, B are in parallel Fig. (iii) 38 THE ALGEBRA OF CIRCUITS 39 where the current passes through A or B or both, and we say that A, B are in parallel. A' is defined as 'not-A' and so A' is on/off when A is off/on.

Then A. B = A. 28? Prove it. 13/1 Exercise. From the statements: (i) All racing motorists are quick-witted. (ii) Plato was a profound thinker. 3 58 A BOOLEAN ALGEBRA (iii) All philosophers are profound thinkers. (iv) Nobody is both quick-witted, and also a profound thinker. can it be deduced that: (a) Plato was a philosopher (b) , , not a racing motorist? Prove your deductions. 13/3 bers: = 2n - 1} is the soa positive odd numbers {x I x = n2 } is the soa squares Exercise. Express in this notation the following sets of num- (i) 1, 2, 4, 8, 16, ..

9 We can apply our algebra to obtain circuits which will perform addition and subtraction of numbers, but first the numbers must be expressed in the binary scale. An ordinary number in the decimal scale is where the D's are the digits of the number, and they take integral values from 0 to 9. A number in the binary scale is where the A's are the digits, and have value 0 or 1. Example. Express the number of days in a year as a binary number, and the binary number 100101011 as a decimal number. 365 = 256 + 64 + 32 + 8 = 1 .

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A Boolean Algebra: Abstract and Concrete by A.P. Bowran

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