What Is Digital
Extract from the book 'Digital Technology'
Digital is synonymous to counting or computing with numbers based on a digit, hence the word digital. In earlier days when commerce was limited to a much simpler means of bartering, man used his fingers to count and perform numeric computations.
In the early days of computing the decimal system was used but proved difficult to initiate in computers due to its complexity of design. Today, computers use a binary numeral system where counting and calculations are accomplished using the two symbols 0 and 1. By building various logic circuitry complex computers can be produced with the capacity of advanced computations such as landing a spaceship on Mars.
To understand binary numbers consider a light switch in a room. Its position determines whether the light is switched on or off. In one position the light is turned on, in the other it is off. This simple analogy of logic circuitry is the fundamental foundation of all digital technology.
Binary and Decimal Numbers
The decimal system uses 10 symbols represented by 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 to count and carry out computations. By combining these symbols in various patterns any numeric number or fraction from the smallest to the largest value can be represented.
The binary numeral system uses the two symbols 0 and 1 for counting and carrying out computations. In digital technology these two symbols are analogous to the logic operating states of OFF and ON. Complex logic circuitry may be constructed by joining electronic switches that emulate these two operating states. Construction of complex digital logic circuitry is discussed later in this chapter.
Counting in Decimal
In the decimal system 10 symbols are fashioned to represent any numeric value. By placing the symbols in a sequential manner any number can be formulated. The rightmost digit represents a number that is multiplied by 1, the digit to its left represents a number multiplied by 10 and the digit to its left represents a number multiplied by 100 (10 x 10) and so forth.
The decimal number 236 represents a value described by the formula shown below.
236 = (2 x 100) + (3 x 10) + 6
Counting in Binary
In the binary system any numeric value can be represented by a sequence of the symbols 0 and 1. Numbers are represented in a similar manner as the decimal system except counting is carried out by using only these two symbols.
| Decimal | Binary |
| 0 | 0 |
| 1 | 1 |
| 2 | 10 |
| 3 | 11 |
| 4 | 100 |
| 5 | 101 |
| 6 | 110 |
| 7 | 111 |
| 8 | 1000 |
| 9 | 1001 |
from the table above the binary sequence ‘101’ represents the decimal value of 5.
The binary numeric system has a digit multiplication factor of 2. With the binary numeric sequence ‘101’, the rightmost digit represents a number that is a factor of 1. The digit to its left represents a number with a factor of 2 and the digit to its left represents a number with a factor of 4.
|
Decimal Numbers |
Computation | 10 x 10 x 10 x 10 | 10 x 10 x 10 | 10 x 10 | 10 | 1 |
| Result | 10000 | 1000 | 100 | 10 | 1 |
|
Binary Numbers |
Computation | 2 x 2 x 2 x 2 | 2 x 2 x 2 | 2 x 2 | 2 x 1 | 1 |
| Result | 16 | 8 | 4 | 2 | 1 |
Comparison of Binary and Decimal Systems
Similar to the decimal system, the binary system represents values that are represented by factors dependent on their sequential position. The binary numeric sequence ‘101’ is symbolic of the decimal value of 5.
(1 x 2 x 2) + (0 x 2) + (1 x 1) = 4 + 0 + 1 = 5
Extract from the book 'Digital Technology'