Building basic Circuits

• Build a circuit for a half adder
  • Two inputs: a,b
  • Two outputs: sum, carry out.
  • Truth table
  • Algebraic expressions
  • Circuit
• Build a full ader
  • Three Inputs: a,b carry in
  • Two outputs: sum, carry out
  • TT, AE, C
  • s = (a xor b) xor c_in
  • c_out = ab + (a xor b)c_in
• Build a component to add two 4 bit numbers.
  • Detect overflow (c_in not the same as c_out in MSB)
  • This is called a ripple carry adder
  • What is the performance of this adder?
• A multiplexor
  • n input bits
  • lg₂(n) control bits
  • 1 output bit
  • Draw circuit.
• A demultiplexor
• How about subtraction
  • Don't forget two's compliment
  • Flip the bits and add one.
• A decoder
  • n input bits
  • 2ⁿ outputs
  • The input selects a single line to raise for output
• A shift circuit
  • numeric input (4 bits)
  • 1 control shift left/not right
  • 1 propagate/not fill bit
  • 1 fill bit
  • numeric output (4 bits)
• ALU
  • two numeric inputs (a,b) (4 bits each)
  • two bit op code
    4 bit output
    1 bit error (on overflow)

    Op Code	Action
    00	ADD
    01	Subtract
    10	Shift a, b3 left/!right b2 prop/!fill b1 fill
    11	Not Defined

• On your own
  • Build an encoder
    • n output bits
    • 2ⁿ input bits, only 1 contains a 1
  • Build a demultiplexor
    • 1 input bit
    • n control bits
    • 2ⁿ output bits
    • The bit is put on the line indicated by the control bits.