### Wednesday, February 23, 2011

## Computer architecture basics

This document is a collection of web pages on computer architecture.

The first part is an introduction to digital circuits. We recommend you read the pages in this order:

- Gates. Here, we introduce the fundamental building blocks of digital computers.
- Truth tables. We discuss truth tables as a way both of describing an existing circuit and of specifying a circuit to be built.
- Combinatorial circuits. We introduce circuits whose output values depend only on a combination of the input values.
- Logic expressions. We explain how to describe circuits as algebraic formulae and how to manipulate those formulae with
*algebraic laws*. - Multiplexer. A particular combinatorial circuit so commonly used that we discuss it separately.
- Demultiplexer. A particular combinatorial circuit so commonly used that we discuss it separately.
- Decoder. A particular combinatorial circuit so commonly used that we discuss it separately.
- Binary arithmetic. In this section, we introduce the fundamentals of binary arithmetic and representation of numbers.
- Circuits for binary arithmetic. We show different circuits for binary arithmetic and explain trade-offs between speed and number of gates.
- Latches and flip-flops. Flip-flops are the basic elements of sequential circuits, the way gates are the basic elements of combinatorial circuits.
- State table. We discuss state tables as a way both of describing an existing sequential circuit and as a way of specifying a sequential circuit to be built.
- Sequential circuits. We introduce circuits whose output values depend not only on the inputs, but also on previous input and output values.
- Registers. A register is a particularly simple sequential circuit that can be instructed to store its input values indefinitely.
- Counters. A counter is a another particularly simple sequential circuit that normally increments its stored value for each clock pulse.
- Binary multiplication. We show how to build a circuit for binary multiplication.
- Tri-state logic circuits. Tri-state logic circuits represent a pragmatic solution to some problems of circuit complexity.
- Buses. With tri-state logic, we can use a
*bus*to transport data. - Memories. While memories are clearly sequential circuits, they have a special structure that makes it interesting to look at them separately.
- Read-only memories. A read-only memory is nothing more than a combinatorial circuit, but often built as a memory.

- Counter with clear. This sequential circuit is nominally an ordinary counter, but an additional input allows us to clear the contents of the counter.
- Counter register. This sequential circuit is a combination of a counter and a register.
- Counter register with clear. This sequential circuit is a combination of a counter with clear and a register.
- Counter register with clear and explicit increment. This sequential circuit is similar to a counter register with clear, except that it does not increment unless explicitly instructed to.
- Micro memory. This is a combinatorial circuit sometimes in the form of a PROM.
- Instruction decoder. This is a combinatorial circuit sometimes in the form of a PROM.
- Arithmetic and logic unit. This is a combinatorial circuit for doing arithmetic and logic operations. The operation can be selected by the value of inputs.
- The first computer. We present our first simple computer, allowing us to make some very simple computations.

- Conditional jumps. So far, our computer could only do unconditional jumps. Now, we show how to introduce conditional jumps as well.
- Subprograms. We add support for procedures and functions in high-level languages and discuss call/return protocols.
- Parameter passing. We add support for passing parameters to subroutines on the stack.
- Local variables We show how to use existing instructions to allocate space on the stack for local variables.
- Interrupts. Our computer must know how to react to external events from timers and peripherals. The mechanism for interrupts makes that possible.