Review topics: Here are the new topics since the second exam. (Note that there will be emphasis on this material, including especially Chapter 6.)

• Exceptions and the trap handler in MIPS (Lab 10).
  • The specifics of how the trap handler works.
  • Review exercise (old quiz): In Postscript, In PDF

• Coding and information theory in computer storage and communications
  • Shannon's information theory
    • Intuitive idea of information = amount of ``surprise'' in a message.
    • Entropy = amount of information in a message.
    • Definition of Entropy. Examples.
    • Idea of Channel Capacity.
  • The three types of coding:
    • Source coding, using data compression.
    • Channel coding, using error detection/correction. This is the area we went into in more detail, including a discussion of the Hamming code to do single-error correction and double-error detection:
      • The idea of a parity check (even parity) using an extra check bit.
      • Assume the message to be corrected by the Hamming code is in bit positions 1, 2, 3, 4, 5, ....
        • The Hamming code uses bits in positions 1, 2, 4, 8, 16, 32, ... for (even) parity checks of selected bits (not all of them).
        • The parity bit in position 1 checks odd-numbered bits (those for which the position number written in binary has a 1 as least significant bit).
        • The parity bit in position 2 checks bits 2, 3, 6, 7, 10, 11, 14, 15, ... (those for which the position number written in binary has a 1 as next-to-least significant bit).
        • The parity bit in position 4 checks bits 4, 5, 6, 7, 12, 13, 14, 15, ... (those for which the position number written in binary has a 1 as second-from-least significant bit).
        • The parity bit in position 8 checks bits 8, 9, 10, 11, 12, 13, 14, 15, 24, ... (those for which the position number written in binary has a 1 as third-from-least significant bit).
        • The parity bit in position 16 checks bits 16, 17, 18, 19, 20, 21, ... (those for which the position number written in binary has a 1 as third-from-least significant bit).
      • We went over an example showing how it works. (See tables at the end for this example.)
      • Add a parity bit in position 0 to check all bits. This gives double error detection as well as single error correction.
      (See Hamming Code Reference.)
    • Secrecy coding, using cryptography.

• Pipelined Implementation (Chapter 6)
  • Overview (Section 6.1, includes especially discussion of hazards).
  • Pipelined datapath (Section 6.2, ignores hazards). Note the several ways of graphically representing pipelines on pages 461-465, especially the series of diagrams in Figures 6.22-6.24.
  • Pipelined control (Section 6.3, ignores hazards). The control signals from the Control unit are the same as for the single-cycle implementation, but the pipelined implementation makes use of extra latched register storage between pipeline stages to pass along control information. (See Figures 6.29 and 6.30. See also the good series of diagrams in Figures 6.31-6.35.)
  • Data hazards and forwarding (Section 6.4). You should understand how forwarding works, with the Forwarding Unit and extra control and data lines. This applies to dependencies between the register result of one instruction and the use of that new register value in subsequent instructions. (See especially Figure 6.38 and the series of diagrams in Figures 6.41-6.42. We did not cover Figure 6.43 or page 488.)
  • Data hazards and stalls (Section 6.5). In case of a dependency involving a lw instruction, the machine must stall for one instruction. This uses the Hazard Detection Unit. Note how the stall is inserted by de-asserting write lines to the PC and the IF/ID registers, and by inserting all zeros on control lines. (These zeros propagate along from cycle to cycle, as the "bubble" of a stalled instruction moves along the pipeline.) See diagrams in Figures 6.47-6.49. Note that the final forwarding is done by the Forwarding Unit as before.
  • Branch hazard (Section 6.6). In case of a branch, if the branch is taken (in one simple implementation), must stall and wipe out the start of the next instruction. (Also need to move branch handling into step 2 of pipeline.) See Figures 6.51 and 6.52. Skip Section 6.6 from pape 501 on.
  • Exceptions (Section 6.7). Example of arithmetic overflow. IF.Flush, ID.Flush, EX.Flush lines to put nop in first stage and to set control lines to zeros in second and third stages.

• Caches (Chapter 7)
  • The general idea of caching, used not just for memory, but with disk storage and elsewhere.
  • SRAM versus DRAM (B.5, pages B-26 to B-33).
  • The idea of hashing, with a hash function and with some method for resolving collisions:
    • Open addressing, that is, using the next available sequential location after the hash address.
    • Bucketting, that is, using a linked list attached to to each hash address.
    • Overflow area. Using an additional area for data that collided.
  • A very simple example, with 3-bit cache addresses, and 5-bit memory addresses. Use the low-order 3 bits of the memory address for the cache address. See Figures 7.5 and 7.6.
  • A simple approach to a cache, involving a cache table such as the one shown in Figure 7.7, with 1024 cache entries (using a 10-bit cache address), indexes in the range from 0 to 1023, a valid bit, a 20-bit tag field, and a 32-bit data field.

    For lookup:

    • The CPU generates an address.
    • Extract a 10-bit index from bits 11-2 of the address.
    • For the address of a word, bits 1-0 will be 0.
    • Compare the 20-bit quantity from bits 32-12 of the address with the tag field. If equal, you have a hit, and return the data field. If not equal, you have a miss; go out to main memory.
    • In case of a miss, stall the CPU, fetch the word from memory, load it into the cache, and restart the instruction so that this time there will be a cache hit.
  • A very similar but slightly more complicated example as shown in Figure 7.8, with 14-bit cache addresses (16K entries), and a 16-bit tag field. Once again, bits 0 and 1 are not used, since the cache is fetching words.
  • Using spatial locality (which means that if an item is referenced, items whose addresses are close by will tend to be referenced soon): As illustrated in Figure 7.10, each cache entry could be a block of 4 words, so that a cache miss will fetch 4 adjacent words, leading to likely hits afterwards.
  • Associative caches, as illustrated in Figure 7.19, where 4 completely distinct words are held for each cache index (4-way associative).

Likely final exam questions:

• No questions about the use of CMOS transistors to create gates.
• Probably several questions about MIPS assembly and machine language. I might ask for the code for a simple loop (use of beq or bne), or for a simple call to a function (jal) and the code for the function (jr $ra to return), or access to memory (use of lw or sw). I might ask you to unravel machine code.
• At least one question on either the single-cycle or multi-cycle implementation. This might even ask you to do something creative, such a implementing a new instruction. The text has exercises asking how to implement the addi instruction in both the single-cycle and the multi-cycle models, without additional control lines. (Instruction decode does have to recognize the new instruction.)
• Extra emphasis on the pipelining chapter, the first seven sections.
  • I might ask about the pipelined datapath or pipelined control (lots of figures in sections 6.2, 6.3).
  • I plan to give you a diagram with a forwarding unit, for you to explain how the forwarding unit works in simple cases not involving a stall (section 6.4, figures 6.41, 6.42).
  • I might ask about the hazard detection unit and stall used to handle the lw instruction (section 6.5, figures 6.47, 6.48, 6.49).
  • I might ask about handling the beq instruction by moving everything into step 2, and by putting in a 1-cycle stall bubble (for successful branch) (section 6.6, figures 6.51, 6.52).
  • I might ask about handling arithmetic overflow exception by flushing the pipeline and restarting the instruction at address 40000040 (section 6.7, figures 6.55, 6.56).
• Probably one question about exception handlers.
• Definitely one question about coding theory, probably the Hamming code.
• Definitely one question about hashing or cache memory.

Good Luck!!!