by irisxzy

How Computers Add Numbers

 Transistor

  • Transistors have two basic functions in computer science:conducts electricity or blocks the flow of electricity, depending on the voltage level of an input signal.
  • Transistors are made of semiconductor material (like silicon).
  • Semiconductor materials such as silicon that is neither a good conductor(copper) nor a good insulator(rubber)
  • Transistors act like a switch although they do not have moving parts.
  • 3 Terminals:
    • Source: produce electricity for light, etc.
    • Base: a gate between the source and ground. Only if the based is charged, source and ground are connected.
    • Emitter, typically connected to a ground wire
  • When base is charged, the electrical signal is grounded, and it flow through an alternative route to the ground.
  • When base is uncharged, the electrical signal flows through an alternative route to the ground.
屏幕快照 2016-09-23 下午10.08.45.pngA Transistor (Dale and John)

 

NOT Gate Constructed by Transistor: Inverted

屏幕快照 2016-09-23 下午10.22.50.png(Dale and John)
  • When source and Vin are charged(Vin is 1), electrical signal is grounded, Vout is 0.

NAND Gate Constructed by Transistor:

屏幕快照 2016-09-23 下午10.23.01.png(Dale and John)
  • When source, V1, V2 are charged(V1 and V2 are 1); electrical signal is grounded, and Vout is 0.

NOR Gate Constructed by Transistor

屏幕快照 2016-09-23 下午10.23.09.png(Dale and John)

Circuit

  • Combinational circuit
    • Boolean expression (AB+AC)
%e5%b1%8f%e5%b9%95%e5%bf%ab%e7%85%a7-2016-09-23-%e4%b8%8b%e5%8d%8810-46-22%e5%b1%8f%e5%b9%95%e5%bf%ab%e7%85%a7-2016-09-23-%e4%b8%8b%e5%8d%8810-47-02
(Dale and John)
  • Sequential circuit
    • Boolean expression A(B + C)
%e5%b1%8f%e5%b9%95%e5%bf%ab%e7%85%a7-2016-09-23-%e4%b8%8b%e5%8d%8810-50-55%e5%b1%8f%e5%b9%95%e5%bf%ab%e7%85%a7-2016-09-23-%e4%b8%8b%e5%8d%8810-51-04
(Dale and John)

Circuit equivalence

  • The same output for each corresponding input–value combination for two circuits

Properties of Boolean algebra

屏幕快照 2016-09-23 下午10.53.35.png
(Dale and John)

Adder

  • Adder is a electronic circuit that performs an addition operation on binary values
  • Half adder: A circuit that computes a sum of two bits by using XOR Gate (A⊕B) and a carry bit by using AND Gate (AB). For example, if the inputs are 1 and 0, the sum will be 1 and the carry bit will be 0. If the inputs are 1 and 1, the sum will be 0 (since binary system base 2), and the carry bit will be 1.
屏幕快照 2016-09-23 下午10.56.21.png(Dale and John)
  • Full adder A circuit that computes a sum of two bits, an input carry bit (carry-in bit) into account, and two carry-out bits. 
    %e5%b1%8f%e5%b9%95%e5%bf%ab%e7%85%a7-2016-09-23-%e4%b8%8b%e5%8d%8810-56-29(Dale and John)

    Circuit as Memory

    屏幕快照 2016-09-23 下午11.03.26.png(Dale and John)
  • sequential circuit
  • Two complementary outputs X and Y (0 or 1)
  • Value of X: current state of the circuit. (If X is 1, the circuit is storing a 1; if X is 0, the circuit is storing a 0.)
  • External input (S or R) and one input coming from the output of the other gate.

Work Cited

Dale, Nell and John Lewis. Computer Science Illuminated. Print.

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