You should be able by now to write Boolean expressions from Logic Gate circuits or construct circuits from Boolean expressions, construct truth tables and prove equality of Boolean expressions using truth tables. Operators to be used are AND, OR, XOR, NOT, NAND, NOR.

1. Click to the link here for your homework Exercises 5  to be delivered on Tuesday 23/10.

2. Here is an introduction for the gates for further reading click here 1

                                                                                            click here 2
                                                                                            click here 3


Summary
logic gate is a circuit which uses digital signals as its inputs and outputs. What makes a circuit a gate is that each output depends entirely on the signals applied at the inputs. If these input signals change, then the output signal may also change. Digital circuits  which use logic gates are usually arranged so that a logic 1 appears at an output only for some definite combination of input signals - for this reason these circuits are sometimes called combinational logic circuits. In theory, we could make i.c.s for each and every possible combination of input signals to produce a 1 output, but this would be wasteful of resources. In practice, what is done is to make i.c.s which accomplish a few standard logic operations. 


From these standard logic i.c.s any combinational logic circuit can be built up. The microprocessor is an extension of this idea - a circuit which can perform virtually any logic function. 

The action of a standard combinational logic circuit, or of any circuit made up from these units, can be described in two ways. 

  • One way is by the use of a truth table. A truth table shows what output can be expected from each possible combination of inputs, so that the action of the circuit can be readily checked. 
  • Another method of describing the action of a circuit is by Boolean Algebra . This method is much more concise but less easy for the raw beginner to interpret.



 Boolean algebra, incidentally, was invented long before modern computers. It is named after George Boole (1815-1864) who devised it as a method of turning logical statements into algebraic expressions. Little use was made of this work until Shannon found in 1938 that Boolean algebra could be usied to analyse relay circuits which carried out the sort of switching operations we now refer to as 'AND' and 'OR' gates.
 


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