Logic Gates and Truth Tables

Logic gates are the atoms of digital hardware. Every processor, memory and accelerator is, at the bottom, millions of these few primitive gates wired together. This chapter defines each gate by its truth table and shows them running.

The primitive gates

AND outputs 1 only when all inputs are 1. OR outputs 1 when any input is 1. NOT (inverter) flips its input. XOR outputs 1 when the inputs differ — the basis of adders and parity. NAND and NOR are AND/OR followed by inversion and are functionally complete: any logic function can be built from NAND gates alone, which is why silicon libraries lean on them.

The testbench sweeps all four input combinations and prints the truth table for every gate at once:

module tb;
  reg a, b;
  initial begin
    $display(" a b | AND OR XOR NAND NOR");
    {a,b}=2'b00; #1 $display(" %b %b |  %b   %b   %b   %b    %b", a,b, a&b, a|b, a^b, ~(a&b), ~(a|b));
    {a,b}=2'b01; #1 $display(" %b %b |  %b   %b   %b   %b    %b", a,b, a&b, a|b, a^b, ~(a&b), ~(a|b));
    {a,b}=2'b10; #1 $display(" %b %b |  %b   %b   %b   %b    %b", a,b, a&b, a|b, a^b, ~(a&b), ~(a|b));
    {a,b}=2'b11; #1 $display(" %b %b |  %b   %b   %b   %b    %b", a,b, a&b, a|b, a^b, ~(a&b), ~(a|b));
    $finish;
  end
endmodule

a b | AND OR XOR NAND NOR
 0 0 |  0   0   0   1    1
 0 1 |  0   1   1   1    0
 1 0 |  0   1   1   1    0
 1 1 |  1   1   0   0    0