Analog Versus Digital

Kuliah Sistem Digital, Teknik Elektro UMY(Rahmat Adiprasetya)

Concept

Electronic engineers split their world into two views called analog and digital

A digital quantity is one that can be represented as being in one of a finite number of states, such as 0 and 1, ON and OFF, UP and DOWN, and so on

Digital and Analog Waveform

Digital and Analog Views (1)

Digital and Analog Views (2)

Digital and Analog Views (3)

The Transistor as a Switch (1)

To illustrate the application of a transistor as a switch, first consider a simple circuit comprising a resistor and a real switch

The Transistor as a Switch (2)

Now consider the case where the switch is replaced with an NMOS transistor whose control input can be switched between VDD and VSS

Alternative NumberingSystems

Decimal (Base-10) The commonly used decimal numbering system is

based on ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The name decimal comes from the Latin decem, meaning “ten.”

The decimal system is a place-value system, which means that the value of a particular digit depends both on the digit itself and its position within the Number

Decimal (Base-10)

Decimal (Base-10)

Decimal (Base-10)

Duo-Decimal (Base-12)

Some cultures made use of duo-decimal (base-12) systems; instead of counting fingers they counted finger-joints.

This form of counting may explain why the ancient Sumerians, Assyrians, and Babylonians divided their days into twelve periods, six for day and six for night

Duo-Decimal (Base-12)

If a similar finger-joint counting strategy is applied to both hands, the counter can represent values from 1 through 24

This may explain why the ancient Egyptians divided their days into twenty-four periods, twelve for day and twelve for night

Sexagesimal (Base-60) The ancient Babylonians used a

sexagesimal (base-60) numbering system. This system, which appeared between 1900 BC and 1800 BC, is also credited as being the first known place-value number system.

Sixty is the smallest number that can be wholly divided by 2 through 6; in fact, sixty can be wholly divided by 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30. Just to increase their fun, in addition to using base sixty the Babylonians also made use of six and ten as sub-bases.

The Concepts of Zero and Negative Numbers

The concept of numbers like 1, 2, and 3 developed a long time before the concept of zero. In the original Babylonian system a zero was simply represented by a space

In fact, it was not until around 600 AD that the use of zero as an actual value first appeared in India.

Vigesimal (Base-20)

The Mayans, Aztecs, and Celts developed vigesimal (base-20) systems by counting using both fingers and toes.

For example, to say fifty-three, the Greenland Eskimos would use the expression “Inup pinga-jugsane arkanek-pingasut,” which translates as “Of the third man, three on the first foot.

To this day we bear the legacies of almost every number system our ancestors experimented with.

From the duo-decimal systems we have twenty-four hours in a day (2 × 12), twelve inches in a foot, and special words such as dozen (12) and gross (144).

Similarly, the Chinese have twelve hours in a day and twenty-four seasons in a year.

From the sexagesimal systems we have sixty seconds in a minute, sixty minutes in an hour, and 360 degrees in a circle.

This all serves to illustrate that number systems with bases other than ten are not only possible, but positively abound throughout history.

Quinary (Base Five)

One system that is relatively easy to understand is quinary (base-5), which uses the digits 0, 1, 2, 3 and 4.

This system is particularly interesting in that a quinary finger-counting scheme is still in use today by merchants in the Indian state of Maharashtra near Bombay.

Quinary (Base Five)

Binary (Base-2)

Base-2 number systems are called binary and use the digits 0 and 1.

As usual, each column in a binary number has a weight derived from the base, and each digit is combined with its column’s weight to determine the final value of the number

Binary (Base-2)

Binary (Base-2)

Although binary mathematics is fairly simple, humans tend to find it difficult at first because the numbers are inclined to be long and laborious to manipulate.

For example, the binary value 110100112 is relatively difficult to conceptualize, while its decimal equivalent of 211 is comparatively easy.

Binary (Base-2)

On the other hand, working in binary has its advantages. For example, if you can remember . .

. . . then you’ve just memorized the entire binary multiplication table!

Octal (Base-8) and Hexadecimal (Base-16)

Any number system having a base that is a power of two (2, 4, 8, 16, 32, etc.) can be easily mapped into its binary equivalent and vice versa.

For this reason, electronics engineers typically make use of either the octal (base-8) or hexadecimal (base-16) systems.

Octal (Base-8) and Hexadecimal (Base-16)

Each octal digit can be directly mapped onto three binary digits, and each hexadecimal digit can be directly mapped onto four binary digits

Octal (Base-8) and Hexadecimal (Base-16)

Representing Numbers Using Powers

Representing Numbers Using Powers

Representing Numbers Using Powers