Page 124 - Bebop to The Boolean Boogie An Unconventional Guide to Electronics Fundamentals, Components, and Processes

Using Primitive Logic

Functions to Build More

Complex Functions

The primitive functions NOT, AND, OR, NAND, NOR, XOR, and
XNOR can be connected together to build more complex functions which
may, in turn, be used as building blocks in yet more sophisticated systems.
The examples introduced in this chapter were selected because they occur
commonly in designs, are relatively simple to understand, and will prove useful
in later discussions.

Scalar versus Vector Notation

A single signal carrying one bit of binary data is known as a scalar entity.
A set of signals carrying similar data can be gathered together into a group
known as a vector (see also the glossary definition of “vector”).

j *m2: I
I

I I I
I Gate 3 I I Gate [3] I I Gate [3:0] I
I I I I 4
I I I -+--
I
: +-E Y2 I I Y[21 j I Vector Notation
I
I I I I (Compressed)
I I I Gate [2] I
I Gate 2 I I I
I I I I I
~ +--Ed! YUI j
I
I
I I I
I I I I
I Gate 1 I I I I Gate [I] I I
j +-EA! Y[OI I I I
I
I
I
I
I
I
I I
I I I I
I Gate 0 I I Gate [O] I
I I I I
I I I I
I I I I
l-_-_________________I
Scalar Notation Vector Notation Figure 11-1: Scalar
(Expanded) versus vector notation