Computer Systems Org I - Prof. Grishman

Lecture 26 - Dec. 3, 2005

Computer logic (P&P chapter 3)

Ripple-carry adder

To add n bits, we connect together n adders.  The rightmost adder can be either a half adder or a full adder with the carry-in permanently tied to 0.  The adders are connected together with the carry out of one bit feeding the carry in of the next bit, as shown on p. 63 of P&P.

Multiplexer

A multiplexer selects one of two inputs (or, more generally, n inputs) and sends that to the output.  The circuit for a two-input multiplexer is shown on p. 61 of P&P.

ALU

An ALU (Arithmetic-Logic Unit) takes two n-bit inputs and a function input, and computes one of a small number of arithmetic or logical functions of the two inputs.  The ALU is the heart of any computer.  For the LC-3, it has to compute three functions:  ADD, AND, and NOT.

The design of an ALU is very simple:  we build a separate circuit for each.  Then we build a multiplexer which selects the output of the appropriate circuit.

Storage Element (P&P 3.4)

A storage or memory element is different from a combinational circuit ... its output is not a function of its current inputs alone.  It is able to store (retain) information.

The gated D latch (P&P 3.4.2) is able to store one bit;  it has a data input and a write enable (clock) input.

A register (3.4.3) is a bunch of such latches with a common write enable input.