• A bunch of logic gates combined
    • Output of one gate --> input of another
    • Flow of electricity is controlled by the interacting gates
  • Equivalent when they produce the same output for identical input

Combinational Circuits

  • Circuit whose output is solely determined by its input values

Sequential Circuits

  • Circuit whose output is a function of its input values and the current state of the circuit


  • Performs addition operation on binary values

Half Adder

Half adder logic diagram

  • Computes the sum of two bits and produces the appropriate carry bit
  • An XOR and an AND gate
  • Doesn't allow a possible carry coming in the calculation

Full Adder

Full adder logic diagram

  • Computes the sum of two bits, taking an input carry bit into account


  • Input control signals determine which input is routed to its output
    • Many input lines
  • Often called a mux
  • Values on $n$ input control lines determine which of $2^n$ other data lines are selected for output
  • Demultiplexer (demux) is the opposite of a mux
    • Single input --> one of $2^n$ outputs depending on values of $n$ control lines

Circuits as Memory

  • Can store information
  • Sequential circuit
    • Output serves as input
    • Existing state of circuit is used to determine next state

S-R Latch

S-R latch

  • Stores single bit
  • Guarantees two outputs ($X$ and $Y$) are always complements of each other

Integrated Circuits

Example of an SSI chip

AbbreviationNameNumber of Gates
SSISmall-scale integration1 to 10
MSIMedium-scale integration10 to 100
LSILarge-scale integration100 to 100,000
VLSIVery-large-scale integration>100,000

Electricity Computer Science