Hello World! An Invitation to Computer Science

Lecture Slides

Control and Memory Circuits
and the Von Neumann Architecture
Monday, March 3, 2008

Key ideas from last time

• truth table can represent any (binary) function
   need not model real world, or anything in particular
   on the other hand, it can be effective
    descriptive, not algorithmic
• can apply sum-of-products algorithm
• can then translate Boolean expressions to circuits
• but is this always practical?

Control circuits

• so far: circuits to do "sequential" operations
• now we need circuits for conditionals and iteratives
• same truth-table techniques apply
    first we need to think of control as logic

Conditional as Boolean expression

  if c then s else t

 c  s  t   out     product terms
-----------------------------------------------
 0  0  0    0
 0  0  1    1      (NOT c) AND (NOT s) AND t
 0  1  0    0
 0  1  1    1      (NOT c) AND s AND t
 1  0  0    0
 1  0  1    0
 1  1  0    1      c AND s AND (NOT t)
 1  1  1    1      c AND s AND t

  (c AND s) OR ((NOT c) AND t)

this is 1-bit multiplexor

this idea scales, as well

Binary → unary

decodertakes n-bit binary-coded input
  and turns on exactly one of 2ⁿ lines

 ins     outs
 a  b   c  d  e  f
 ----   ----------
 0  0   1  0  0	 0   c = (NOT a) AND (NOT b)
 0  1   0  1  0	 0   d = (NOT a) AND b
 1  0   0  0  1	 0   e = a AND (NOT b)
 1  1   0  0  0	 1   f = a AND b

Iterative operations

• problem: we need to count
• we can build circuits to add and compare
• how do we remember what number we are at?
• we need memory

Strange loops

• idea: use a feedback loop
• essentially have circuit saying:
    "I am on, I am on, I am on, ..."
• first attempt: feedback through OR:
  
• but how to turn it off?

Toggle flip-flop

input     output
 t   old   new
 -------------
 0   0    0
 0   1    1
 1   0    1
 1   1    0

Just an XOR ... with feedback!

Abstraction hierarchy

• zooming in and out
• avoiding being overwhelmed by detail
• switches & wires → gates → integrated circuits

von Neumann architecture

• common among most computers, over 50+ years
• 5 components (focus on: ALU, memory, control)
• sequential execution of instructions:
    fetch from memory, then execute
• stored-program concept

Memory

• RAM: constant-time access to any address
    can be built as array of flip flops
• ROM v. general case
• bits-per-cell (memory width): standard 1 byte (8 bits)
• can use consecutive cells to represent larger quantities
• addresses v. data
    accidental confusion can be source of bugs
    but also gives stored-program concept its power
• load (nondestructive fetch) and store (destructive)
• von Neumann bottleneck and caches

Input and output

• like memory has notion of fetch and store
• volatile v. non-volatile memory
• disk drives:
    sectors, tracks, heads
    seek, latency, transfer times
• sequential devices
• displays, printers, keyboards, etc.
• I/O much slower than other operations
• buffers, controllers, and interrupts