TABLE OF CONTENTS Ian Grout
In everyday life, we use the decimal number system (base, or radix, 10), which allows the creation of numbers with digits in the set: 0, 1,2, 3, 4, 5, 6, 7, 8, 9. The ten possible digits are combined to create integer and real numbers. However, base 10 is not the only number system. Digital circuits and systems use the binary (base, or radix, 2) number system, which allows for the creation of numbers with digits in the set: 0, 1.
The 0 and 1 numbers are logic levels (0 = logic 0, 1 = logic 1), which are created by voltages in a circuit:
In positive logic, 0 is formed by a low voltage level, and 1 is formed by a high voltage level.
In negative logic, 0 is formed by a high voltage level, and 1 is formed by a low voltage level.
In this text, only positive logic will be used and will use the voltage levels shown in Table 8.1.
| Logic level | +5V logic | +3.3V logic |
|---|---|---|
| 0 | +5.0V | +3.3V |
| 1 | 0V | 0V |
Decimal and binary number systems are only two of four number systems used in digital circuits and systems:
decimal (base 10)
binary (base 2)
octal (base 8)
hexadecimal (base 16)
At some point in the design and analysis of a digital circuit, it will be necessary to convert between the different number systems to view and manipulate values propagating through...
