Combinational Logic; Hierarchical Design and Analysis

Tom Kelliher, CS 240

Feb. 17, 2010



Collect assignment.


Read 3.3.

From Last Time

IC technology.


  1. Combinational logic.

  2. Hierarchical design

  3. Design analysis.

Coming Up

Design example.

Combinational Logic

  1. Definition: Logic circuits in which the output(s) depend solely upon current inputs.

  2. No feedback or memory.

  3. Sequential circuits: outputs depend upon current inputs and previous inputs.

    Memory or registers.

  4. Example -- BCD to 7-segment decoder:


Hierarchical Design

  1. Transistor counts:

    Device Count Year
    TI SN7400 16 1966
    Intel 4004 2.3 K 1971
    Intel 8088 2.9 K 1979
    Intel Pentium 3.1 M 1993
    Xilinx Virtex 70 M 1997
    Intel Pentium 4 42 M 2000
    Xilinx Virtex-4 1 B 2004
    Sony Cell 241 M 2006
    Intel Core 2 Duo 291 M 2006
    Intel 6-core Xeon 7400 1.9 B 2008
    Altera Stratix IV 2.5 B 2008
    AMD HD5800 2.154 B 2009
    Intel 8-core Xeon Nehalem-EX 2.3 B future
    NVIDIA GF100 2.9 B future

  2. Design and conquer:

    $\rm CPU \Rightarrow Integer~Unit \Rightarrow Adder \Rightarrow
binary~full~adder \Rightarrow NAND~gates$

  3. Reuse:

    Once logic is collected into a block, it can be instantiated several times in several places.

    Adders are used at several points within a CPU: integer ALU, program counter incrementer, multiplier, etc.

    Binary full adders are connected to form adders.

  4. Scaling:

    Consider the two-dimensional tiling of memory cells.

These techniques reduce the number of transistors which must be laid out ``by hand.''

Design styles:

  1. Top-Down design: divide and conquer.

  2. Bottom-Up design: promotes reuse.

The savvy designer often uses both techniques within a single project.

Design tools:

  1. CAD tools: programs to assist with schematic capture, HDL entry, synthesis, simulation. Running on ``first silicon.''

    The ``old'' days: drafting tables, taping out a circuit, and lots of prototyping.

  2. HDLs and synthesis
    1. Why VHDL is my favorite acronym.

    2. What is VHDL? 4-1 mux example:
      library ieee;
      use ieee.std_logic_1164.all;
      entity mux4_1 is
         port (a0: in bit;
               a1: in bit;
               d0: in bit;
               d1: in bit;
               d2: in bit;
               d3: in bit;
               z: out bit);
      end mux4_1;
      architecture behavioral of mux4_1 is
      signal address: bit_vector(1 downto 0);
         address <= a1 & a0;
         with address select
            z <= d0 when "00",
                 d1 when "01",
                 d2 when "10",
                 d3 when "11";
      end behavioral;

    3. Synthesis process:


Design Analysis

Combinational circuit analysis -- ``reverse engineering.'' Skip.

Logic Simulation:

  1. Vital today: First silicon must run.

    Can't re-wire a die.

    Entire computers have been simulated to the point of booting the OS.

  2. Simulator used to verify circuit behavior and timing.

    Results are only as good as the tests run.

    Large circuits cannot be simulated completely. Just ask Intel (fdiv).

  3. Netlist used to describe circuit. Text file.

  4. Schematic: graphical representation of circuit. Tool to convert to netlist form.

  5. User produces ``test vectors,'' which are the inputs to the simulator.

    Good test vectors are the key to meaningful results.

Thomas P. Kelliher 2010-02-16
Tom Kelliher