1.1 Introductory Concept

There are two fundamental ways to represent the numerical value of quantities: analog and digital. Analog quantities can vary continuously, while digital quantities are represented by discrete symbols called digits.

The response of a digital circuit to an input is known as its "logic". Every type of digital circuit adheres to a specific set of logic rules, leading to them also being referred to as "logic circuits".

Digital devices, such as computers, contain electronic circuits that can rapidly switch on and off. When a circuit is on, it represents a value of 1, and when off, it represents a value of 0 in the binary number system. Digital devices execute mathematical operations by manipulating these switches according to the rules of binary arithmetic.

All instructions that control computer functions and all data manipulated by computers are initially converted into binary numbers to enable more efficient and quicker processing. Digital devices are designed to perform mathematical operations as fast as possible. Devices capable of parallel processing can complete multiple operations simultaneously.

The simplicity of binary arithmetic, combined with the rapid rate at which a computer can manipulate binary data, makes binary numbers ideally suited for computational processes.

A digital system is a combination of devices engineered to manipulate physical quantities or information represented in digital form. Computers and calculators are examples of more common digital systems.

Figure 1 Block Diagram of a digital computer

A computer is a swift and precise information processing system. It is designed to take in, store, and process data, ultimately generating desired outputs under the guidance of a stored set of instructions.

The increasing adoption of digital technology can be attributed to several factors, including but not limited to:

1. Ease of design for digital systems.

2. Simplified information storage

3. Enhanced accuracy and precision.

4. Programmable operations.

5. Reduced susceptibility of digital circuits to noise.

The ability to integrate more digital circuitry onto integrated circuit (IC) chips.

Computers and other digital systems rely on circuits that process information encoded as numbers, such as binary, octal, or hexadecimal. These numbers are then manipulated using logic circuits. Furthermore, digital systems can also represent non-numeric data, events, and various conditions.

The table below shows a comparison among the different number systems.

Table 1. Number Systems

Number System	Base or Radix	Digits	Main Use
Decimal	10	0,1,2,3,4,5,6,7,8,9	Everyday business
Binary	2	0, 1	Internal representation
Octal	8	0,1,2,3,4,5,6,7	Convenient form for input and output device
Hexadecimal	16	0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F	Convenient form for input and output device

The "radix" or "base" of a number system specifies the total count of distinct symbols it uses. Notably, the highest-value symbol in any system will always be one less than its radix.

The base is typically shown as a subscript next to a number, indicating how many unique digits are available in that system. For example, the decimal system, with a base of 10, uses ten unique digits (0-9). The binary system, having a base of 2, uses only two digits (0 and 1). Hexadecimal, with a base of 16, includes digits 0-9 and letters A-F, where A represents 10, B is 11, and so on, up to F for 15.

Ambiguity can arise when representing numbers across different systems. For instance, the decimal number 11 is equivalent to 1011 in binary. To avoid this confusion, a subscript is used to denote the base. So, the binary representation would be written as 1011₂, and the decimal as 11₁₀ .

Important Note: If no subscript is present, a number is generally presumed to be in the decimal system.