1. For question 1, answer the following digital logic questions. (Questions invo

Question

1. For question 1, answer the following digital logic questions. (Questions involve concepts on Digital logic/digital systems, number representation, truth tables and logic functions, logic circuits, boolean algebra, canonical forms, and k-maps)

• What do we mean by the term “digital”?

• Why should we care about digital logic and designing digital systems?

• What is the difference between digital and non-digital systems? What are the advantages and disadvantages of digital systems?

• Why do we use binary values in the design of digital systems?

• Why are octal and hexadecimal formats important to the design of digital systems?

• What are the advantages and disadvantages of complement number systems (i.e. 1’s and 2’s complement) vs. signed-magnitude?

• How many two-input logic functions are there and can you list them?

• Why is it preferable to use NAND and NOR gates in the design of logic circuits? When are NAND and NOR gates not useful?

• What are the advantages and disadvantages of the ideal and delay model timing diagrams? How do they compare with one another?

• What is the importance of the duality principle?

• What is the importance of DeMorgan’s theorem?

• Why is it useful to be able to derive the complement of a Boolean function?

• How are the canonical forms related to a truth-table or a K-map?

• Do you understand the structure of a K-map and how the cells of a K-map are related to one another? Why is this relationship between cells important? Do you understand how the K-map reduces logic expressions?

Explanation / Answer

1. Digital defines electronic system where only two finite states are used to represent any information. A series of 1's and 0's are used to represent logic HIGH /TRUE and LOW/FALSE states.

2. Digital information systems offers ease of storing/retrieving/processing huge amount of data in small memories. Important advantage of digital system is ease of porting data over memory or wired or wireless transmission line. Most of the processing algorithms running on computers work on digital information only.

3. In digital systems there is only two levels / finite levels to represent any real time information where as most of the non digital systems are analog and represented by continuous set of information. Noise immunity is much better in digital systems because of finite levels of information and also error correction , prediction can be implemented easily on a digital data transmitted.

Advantage:

(i) Ease of Portablity

(ii) Flexible and compatible

Disadvantage

(i) Introduces quantization error

(ii) More energy consumption and heat dissipation

4. Digital system comprises of logic gates and only binary information can be processed on these logic gates. If we work on any other data representation like hexadecimal/octal etc then still the information is processed at binary level.Hence working on binary numbers keeps the design much closer to actual hardware instead of working at higher level of abstraction keeps the designer unaware about the actual implementation.  

5. Octal and Hexadecimal numbers uses fewer digits compared to binary number system

6. 1's and 2's complement of a number helps to perform substraction by addition. Hence less hardware required.

7. AND, OR, NOT, EXOR, EXNOR, NAND, NOR

8. NAND and NOR are universal gates and it is possible to implement other logic functions using either NAND or NOR logic. Hence same type of logic gate needed.

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