By Gerard O'Regan
This finished ebook offers an advent into the most important issues within the background of computing in an easy-to-follow and concise demeanour. It doesn't require stories in laptop technology with a view to be understood and preferred. The e-book covers major parts and occasions within the box from the beginnings of computation in 3000B.C. via to the current day. priceless pedagogical parts resembling routines and bankruptcy summaries are incorporated. targeting the basic parts within the computing box, this essentially written and broad-ranging textual content will seize the eye and enormously profit desktop technological know-how scholars.
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Similarly, if z = goats then y + z represents the class that are either sheep or goats. , in a manner that is similar to real numbers. Boole showed how these symbols could be used to reduce propositions to equations, and algebraic rules could be used to solve the equations. The algebraic rules satisfied by his system included: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. x +0= x x + (y + z) = (x + y) + z x+y =y+x x + (1–x) = 1 x1 = x x0 = 0 x +1=1 x y = yx x(yz) = (x y)z x(y + z) = x y + x z x(y–z) = x y–x z x2 = x xn = x (Additive Identity) (Associativity) (Commutativity) (Not operator) (Multiplicative Identity) (Commutativity) (Associativity) (Distributive) (Distributive) (Idempotent) These operations are similar to the modern laws of set theory with the set union operation represented by “+”, and this is the “or” operation in modern Boolean algebra.
4). That is, if the input is “1” the value “0” is returned and vice versa. The NOT gate may be combined with the AND or the OR gate to yield the NAND gate (NOT AND) or the NOR gate (NOT OR). The power of the AND, OR and NOT gates may be seen in the example of a half adder in Fig. 5. It shows how these gates may be combined to do elementary binary arithmetic. The addition of 1 + 0 is considered. The inputs to the top OR gate are 1 and 0 and this yields the result of 1. The inputs to the bottom AND gate are 1 and 0 which yields the result 0, which is then inverted through the NOT gate to yield Fig.
The Romans developed a cumbersome number system that is still used in clocks today. They also developed the Julian calendar and employed simple ciphers to ensure that information communicated was kept confidential. The Islamic contribution helped to preserve the earlier work of the Greeks, and they also developed mathematics and algebra further. Later Islamic scholars applied algebra to arithmetic and geometry. 1 Introduction This chapter considers various pioneers in the history of computing. These include figures such as Boole, Babbage, Turing, Shannon and Von Neumann.