2.4 Computational Logic

2.4 Computational Logic

1. transistors

   • A tiny switch that is activated by the electronic signals it receives. The digits 1 and 0 used in binary reflect the on and off states of this.
   • A common way to think of transistors is that they are like taps. When a tap is turned on, water coming into the tap is allowed to flow through the tap and to come out.
   • In a transistor, when the "base" input on a transistor has a small current flowing through it, the larger current entering the transistor from the "collector" can flow through to the the "emitter".
   • Inside a CPU, transistors are arranged and configured into circuits to perform operations such as calculations when electricity is passed through them.For example, transistors can be arranged to form an "adder" circuit that can accept two binary numbers and output the sum of their values.
   • Modern CPUs contain over 3 billion transistors, allowing them to performs billions of calculations per second.

2. logic gates

   • Multiple transistors can be arranged together to form more complex "switches" that only allow electricity to flow through if all or some of the transistors are "on".
   • Such arrangements of transistors are called logic gates - they act like gates that only open if certain logical conditions are met.
   • There are three types of logic gate that you must be familiar with at GCSE - AND, OR and NOT logic gates.
     • AND
       • AND gates have two inputs and one output
       • An AND gate will only output current (represented as a 1 on the output) if both inputs are on (also represented as 1s)
       • AND gates are represented in Boolean equations using the symbol ∧ (like an upside-down V)
       • The logical statement "A and B" is represented as A ∧ B
     • OR
       • OR gates have two inputs and one output
       • An OR gate will output current (represented as a 1 on the output) if either or both inputs are on (also represented as 1s)
       • OR gates are represented in Boolean equations using the symbol ∨
       • The logical statement "A or B" is represented as A ∨ B
     • NOT
       • NOT gates have one inputs and one output.
       • NOT gates invert the input so their output is the opposite of the input given.
       • NOT gates are represented in Boolean equations using the symbol ¬
       • The logical statement "not A" is represented as ¬ A

3. logic circuits

   • Logic gates can be combined to form logic circuits that process complex logical statements such as A AND (B OR C).
   • The output of logic statements in brackets becoackets must be evaluated first and the result used in a widme input to 'outer' logical operations.This is just the same as in maths where expressions in brer expression.
   • Conventionally, input labels start at A (A, B, C, etc.) whereas output labels start at Q (Q, R, S, etc.).
   • Logic gates can be combined to form logic circuits that process complex logical statements such as A AND (B OR C).
   • The output of logic statements in brackets become input to 'outer' logical operations.
   • This is just the same as in maths where expressions in brackets must be evaluated first and the result used in a wider expression.
   • Conventionally, input labels start at A (A, B, C, etc.) whereas output labels start at Q (Q, R, S, etc.).

4. evaluating NOT expressions

   • NOT gates are applied to the output of the expression that they are inverting.
   • For example, NOT (A OR B) is shown on the right.
   • Again, the rule holds true: evaluate the expression in brackets and pass it as an input to the outer logic gate.

5. evaluating logic circuits with truth tables

   • Truth tables show each possible combination of inputs and the resulting output.
   • In a complex circuit with multiple gates, it can be helpful to include a column for the output of each gate, as well as the overall output of the circuit.
   • Truth tables should always have 2n rows, where n is the number of inputs. For example, a circuit with three inputs would contain 8 (23 ) rows.

Imágenes y archivos del mapa