CS301: Computer Architecture

Read this chapter on Karnaugh mapping, which is a tabular way for simplifying Boolean logic. There are several ways for representing Boolean logic: algebraic expressions, which use symbols and Boolean operations; Venn diagrams, which use distinct and overlapping circles; and tables relating inputs to outputs (for combinational logic) or tables relating inputs and current state to outputs and next state (for sequential logic). When designing sequential logic, some of the components are memory devices. Cost and processing time are considerations in using memory devices, which can be expensive. To reduce the cost or processing time the logic can be simplified. This simplification can be done using algebraic rules to manipulate the symbols and operations, analysis of the areas inside the circles for Venn diagrams, or Karnaugh maps for input/output tables.

Read this chapter, which describes the design of several components using logic gates, including adders, encoders and decoders, multiplexers, and demultiplexers. This chapter also mentions ladder logic. If you are not familiar with ladder logic, you may also optionally read Chapter 6.1 and 6.2 as a reference. Note that ladder logic is not generally used in computer design and may be omitted. For the one input decoder, note that for a 0 input, the D0 output is a 1 and when the input is a 1, the D1 output is a 1. All the other decoders work the same way. One output line is a 1and the rest are 0's, indicating which binary number has been placed on the input lines. So an input in binary of the number 6 would cause D6 to be a 1.

Read this chapter, which discusses how logic gates are connected to store bits (0s and 1s). Combinational circuits, described in the previous section, do not have memory. Using logic gates, latches and flip flops are designed for storing bits. Groups of flip flops are used to build registers which hold strings of bits. For each storage device in Chapter 10, focus on the overview at the beginning of the section and the review of the device's characteristics at the end of its section. While you do not absolutely need to know the details of how latches and flip flops work, you might find the material of interest. We strongly recommend that you read the details of the design of each storage device, because it will give you a stronger background.

Read this chapter on sequential circuits. Combinatorial circuits have outputs that depend on the inputs. Sequential circuits and finite state machines have outputs that depend on the inputs AND the current state, values stored in memory.