sheshanksk/15eeep203_dc_lab_structure_enquiry

DC Lab

15EEEP203: DIGITAL CIRCUITS LABORATORY STRUCTURED ENQUIRY

Assignment Questions:

Question 01: Gray to Binary and Excess-3 to BCD Code Converters Using NAND Gates

Question 02: Subtractor Using 74153 Multiplexer

1a. Gray to Binary Code Converters Using NAND Gates

Introduction: The reflected binary code or Gray code is an ordering of the binary numeral system such that two successive values differ in only one bit (binary digit). Gray codes are very useful in the normal sequence of binary numbers generated by the hardware that may cause an error or ambiguity during the transition from one number to the next. So, the Gray code can eliminate this problem easily since only one bit changes its value during any transition between two numbers. Gray codes are used in rotary and optical encoders, Karnaugh maps, and error detection. The hamming distance of two neighbors Gray codes is always 1 and also first Gray code and last Gray code also has Hamming distance is always 1, so it is also called Cyclic codes. You can convert a Gray code to Binary number using two methods.

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Circuit Diagram

1b. Excess-3 to BCD Code Converters Using NAND Gates

Introduction: The excess-3 code is a non-weighted and self-complementary BCD code used to represent the decimal numbers. This code has a biased representation. This code plays an important role in arithmetic operations because it resolves deficiencies encountered when we use the 8421 BCD code for adding two decimal digits whose sum is greater than 9. The Excess-3 code uses a special type of algorithm, which differs from the binary positional number system or normal non-biased BCD.

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Circuit Diagram

2a. Half-Subtractor using 74153 Multiplexer

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Circuit Diagram

2b. Full-Subtractor using 74153 Multiplexer

Truth Table

Circuit Diagram