Elements of Computing Systems // 1: boolean logic

Basic logic gates (AND, OR, NAND) are the most atomic building blocks of computers and can quickly be combined to create chips capable of arithmetic.

• Examples of gates: And, Or, Xor, Multiplexer, Demultiplexer, + multi bit versions
• Boolean truth table (each permutation) can be derived from boolean expression, and vice versa
• HDL (Hardware Description Language) used to define logic of chip, which can be handed to manufacturers
  • Those specs typically ran through all test cases
• Bitwise operators - apply operator to each bit in given operands
• Multi-way/Multi-bit inputs work the same but allow M inputs. For a multiplexer/demultiplexer, there need to be log2m inputs to select the right input
  • Log2(3) = 8 === 2 to power of 3 = 8
• Behavioral simulation - implementing logic in conventional code, to test before committing to HDL
• Use of boolean algebra to describe behavior of logic gates articulated by Claude Shannon in 1937. Argued most important MSc thesis in comp sci