1.4.3 Boolean Algebra

• D-type Flip Flops

  • A sequential logic circuit used to store a single bit
  • Two stable states
  • Flipped between using an input signal
  • 2 inputs: control signal and a clock input
  • clock: regular pulse generated by the CPU which is used to coordinate the computer's components
• Full Adders

  • A combination of two half adders that takes a carry bit and two other input bits
  • Returns their sum
  • Returns the new carry as two output bits
• Half Adders

  • Combinational arithmetic circuit
  • Adds two number and produces a sum bit (S) and a carry bit (C) as the output
• Output of a D-type flip flip can only change at a rising edge which is the start of a clock tick

  
• D-type flip flop

  • 4 NAND gates
  • Q is the stored value

  
• Adders

  • logic circuit which adds together the number of inputs which are true
  • outputs this number in binary
  • half and full
• Half Adders

  • Two inputs A and B
  • Two outputs Sum and Carry
  • Formed of two logic gates AND and XOR

  
• Full Adder

  • similar to a half adder but has an additional input
  • 2 XOR gates
  • 2 AND gates
  • 1 OR gate