Transistors

• N-type vs P-type

  • N-type

    With the supply voltage applied to the device, the transistor acts like a closed or connected switch

    

    

  • P-type

    With the supply voltage applied to the device the transistor acts like a open or disconnected switch

    

    

Boolean Logical gates

Check HW2 for gate designs

• De Morgan's Law

  

  

• Conte Bubble Theorem

  

• Larger Gates

  

Combinational Logic

A combination of AND, OR, NOT (plus NAND & NOR), The same inputs always produce same output.

• Decoder

  For a decoder of n bit input, there is $2^n$ output at most.

  

  /t

• Multiplexer

  The basic multiplexer has 1 output, n control lines, and $2^n$ inputs.

  In truth table terms: output is on left, input is at bottom, case fulfills on right

  

• Full Adder

  

  Truth table:

  

Questions and Answers

• Basics
  • Be able to read basic circuits (as presented in CircuitSim) and understand the symbols used for common logic gates and other components
    • Common gates ([N]AND, [N]OR, X[N]OR, NOT, etc.)
    • Splitters
    • Multiplexers, decoders
    • Adders, registers
  • Converting boolean expressions to and from logic gates

• Decoders
  • What is the high-level purpose of a decoder? What are some circumstances where a decoder is useful?
    • Decoders set exactly one output based on which of the input bits are set.
    • A decoder has the property that exactly one of its outputs is 1 and all the rest are 0s. The one output that is logically 1 is the output corresponding to the input pattern that it is expected to detect.
    • Circumstances where a decoder is useful
      • The Decoders were used in analog to digital ==conversion in analog decoders.
      • Used in electronic circuits to convert instructions into CPU control signals.
      • They are mainly used in logical circuits, data transfer.
  • If a decoder has a 5-bit input/selector, what is the maximum number of outputs it can have?
    • $2^5=32$
  • If a decoder has an n-bit input/selector, what is the maximum number of outputs it can have?
    • $2^n$
  • If you need a decoder with 23 outputs, how many input bits do you need?
    • 5 since 4 would only get you 16 outputs
  • Know how to visually trace through circuits containing a decoder (e.g., determine what a combinational circuit using a decoder would output for a given input)

• Multiplexer
  • What is the high-level purpose of a multiplexer? What are some common applications for multiplexers? Where did you need to use multiplexers in Homework 2?
    • Selects between inputs using a selector
    • Multiplexers are used in various applications wherein multiple data need to be transmitted by using a single line (ex: communication system, computer memory, telephone network)
    • In Hw2, muxes were used in the ALU, depending on the code, an arithmetic operation would be performed and outputted.
  • If a multiplexer has an n-bit selector, how many inputs can it have?
    • $2^n$
  • If a multiplexer has 23 inputs, how many selector bits do you need?
    • 5 since next highest power of 2 after 23 is 32
  • If a multiplexer has a 6-bit selector, how many outputs does it have?
    • There is only 1 output no matter the number of selector bits.
  • Know how to visually trace through circuits containing a multiplexer (e.g., determine what a combinational circuit using a multiplexer would output for a given input)