## What is Digital Abstraction in digital design

Digital circuits are abstraction of electronic devices. In computers Information is generally represented by voltages. When the two or more components needs to communicate with each other, the sending component sets a voltage on the wire and receiving component read that voltage. But the problem is there are many sources of noise that can cause the voltage received by the receiving component differ from the voltage sent by the sending component. So we built digital systems that consider range of voltages to be equivalent to provide the largest margin of error. So we map voltage into exactly two levels which are HIGH and LOW. There is a threshold value. Voltages above the threshold consider as 1 and voltages below the threshold consider as 0. We do not have to worry about intermediate values of the signals. In the digital design, reducing the complex analog behavior down to 1 and 0 is called digital abstraction.

We know that computers are digital systems. Analog values convert into digital value, then it can be processed by the computers. Digital signals are discrete both in time and in amplitude. When working with digital signals, we assume bits can only be one or zero. This simplifies the designing process lot.

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## Date Representation

In digital design data is known as physical representation of information. Data can be stored, transmitted and processed. Electronic representation of data can be split into two which is Analog representation and Digital representation.

Analog

Numerical value of the physical quantity is expressed as a continuous range of values between the two expected extreme values.

Digital

Numerical value of the physical quantity is expressed as a finite number of values between the two expected extreme values.

But the noise affects digital signals too. Noise is anything that degrades the signal. As an example a gate could output a 5volt signal but, because of the resistance in a long wire, the signal could arrive at the receiver with a degraded value, like 4.5 volts.

To overcome that there is Noise Margins. Noise margin is the amount of noise that could be added to a worst case output such that the signal can still be interpreted as a valid input.

Noise Margin Level (NM_{L}) = V_{IL} – V_{OL} or V_{OH} – V_{IH.}

Advantage of using Digital

- Higher accuracy
- Simple to implement in hardware (using switching)
- Programmability
- Better noise immunity
- Lots of noise margin
- Easier storage

## Number Systems used in digital design

Since we are going to learn digital design from basic we have study about numbering system very first.

Decimal Numbers

Deci is equals to Ten. So the decimal number has ten digits. (0 1 2 3 4 5 6 7 8 9). The decimal number system has a base of 10, with each position weighted by a power of 10. Whole number part and the fractional part is separated by a decimal point called decimal point.

10 | 10 | 10 | . | 10 | 10 | 10 | 10 | 10 |

Binary Numbers

Bi is equals to two. So the binary number system has two digits which are 0 and 1. The binary number system has a base of 2 with each digit position weighted by a power of 2.

2 | 2 | 2 | 2 | . | 2 | 2 | 2 | 2 |

Hexadecimal Numbers

Hexadeci means sixteen. So they are called base 16 number system. There are 10 digits and 6 letters. (0 1 2 3 4 5 6 7 8 9 A B C D E F). those letters represent the number from 10 to 15. The hexadecimal number system has a base of 16 with each digit position weighted by a power of 16. These are easy to convert to and from binary numbers.

## Number Conversion

Decimal to Binary

There are several methods to convert decimal to binary. One is express the decimal number as the sum of power 2. Then 1s and 0s written in the corresponding bit position.

Example 50_{10} = 32 + 18

= 32 + 16 +2

= 1×2^{5} + 1×2^{4} + 1×2^{1}

^{ }= 110010_{2}

Second is divide method, there are several steps in there

- Divide the number by 2
- Get the integer quotient for the next iteration
- Get the remainder for the binary digit
- Repeat above steps until you get 0 as the quotient.

Divide by 2 | Quotient | Remainder | Bit |

50/2 | 25 | 0 | 1 |

25/2 | 12 | 1 | 2 |

12/2 | 6 | 0 | 3 |

6/2 | 3 | 0 | 4 |

3/2 | 1 | 1 | 5 |

1/2 | 0 | 1 | 6 |

Binary to Decimal

Determine the power of 2 for the position of each 1 and then take the sum.

Example 10101_{2} = 2^{4 }+ 2^{2 }+2^{0} = 16 + 4 +1 = 21

Binary to Octal

In the binary to octal conversion, each octal digit corresponds to three binary digits. Partition the binary number into groups of three digits to the left and to the right from the binary point.

Example 10110001101011.111100000110_{2} convert to octal

010 | 110 | 001 | 101 | 011 | . | 111 | 100 | 000 | 110 |

2 | 6 | 1 | 5 | 3 | . | 7 | 4 | 0 | 6 |

The answer is 26153.7406_{8}

In the binary to hexadecimal conversion we can use the same concept except that the partitioning is of four digits’ groups. Also you can reverse the preceding procedure to get the octal/hexadecimal to binary conversion.

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