
Explore number systems at the heart of digital electronics, including binary, hexadecimal, octal, and decimal. Learn conversion, binary arithmetic, ones and twos complement, and codes like BCD and Hamming code.
Explore how number representation works across binary, octal, decimal, and hexadecimal systems, including radix, positional weights, and digit symbols.
Explore how counting works across decimal, octal, hexadecimal, and binary systems, including digit limits, radix rules, and bit toggling in four-bit and higher systems.
Master converting binary, octal, and hexadecimal numbers to decimal using positional weights, with worked examples and practice questions, and learn why decimal is essential for presenting digital information.
Learn decimal to binary, octal, and hexadecimal conversions by splitting integer and fractional parts; apply division by the base for integers and multiplication by the base for fractions, with examples.
Explore binary to octal and hexadecimal conversions, octal and hex to binary, using grouping by three or four bits and radix point rules, plus decimal conversion basics.
Explore unsigned binary arithmetic: addition, subtraction with borrow, multiplication by shifting, and division, showing how binary rules mirror decimal ones, with a mention of signed numbers.
Master the representation of signed binary numbers in digital electronics through sign magnitude, one’s complement, and two’s complement. Explore zero representations, radix complements, and practical conversions with examples.
Explore binary arithmetic for sign numbers using the one's complement method, including eight-bit representation, end-around carry, and obtaining the correct magnitude by complementing magnitude bits, with subtraction examples.
Explore BCD and excess-3 codes, encoding decimal digits in 8421 BCD and converting between binary, decimal, and BCD. Understand their arithmetic advantages, self-complementing and reflective properties in digital circuitry.
Explore gray code, its advantages for error detection and single-bit transitions, and how to convert between binary and gray codes using XOR, with applications in instrumentation, IoT, and digital communications.
Explore ASCII code, a seven-bit scheme that represents 26 uppercase letters and 26 lowercase letters, 10 digits, and 33 special characters using a lookup table to map characters to binary.
Explore error detecting and correcting codes, including parity checks and checksums. See how odd/even parity and parity bits detect and correct single bit errors and use block parity for localization.
Hamming code acts as an error detecting and correcting code, using p1 through p4 parity bits to locate and fix single-bit errors, with code length n+k.
Explore error detection and correction using hamming codes, with seven-bit parity codes and c1, c2, c3 parity checks to locate and correct single-bit errors at the receiver.
Explore binary, octal, hexadecimal, and decimal representations, unsigned and signed arithmetic, ones and twos complement, parity, checksum, block codes, and seven-bit Hamming code for the message 1010.
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The study of number system is important from the view point of understanding how data are represented before they can be processed by any digital system including digital computers. In a digital system, the data is usually in binary states (0 or 1) and are processed and stored electronically to prevent errors due to noise and interfering signals. Digital circuits find applications in computers which accepts data or information in binary as well as Hexadecimal, whereas in the outside world, we humans commonly use the Decimal System. So, it is highly beneficial to learn all these number systems in detail to progress smoothly to the world of Digital Circuit Design.
Discovering Number Systems used in Digital Circuits.
· Familiarize number representation in different number systems.
· Learn the conversion between different digital formats – Decimal, Binary, octal and hexadecimal number system.
· Study simple binary Arithmetic – Addition, Subtraction, Multiplication and Division of Binary Numbers.
· Learn signed number representation & signed number Arithmetic – One’s and Two’s Complement systems.
· Find different Binary Codes – BCD, Gray, Excess-3, ASCII, Error correcting and detecting codes.
Understanding the principles of number representation, conversion & Binary arithmetic.
A number system is a language system consisting of an ordered set of symbols called digits with rules defined for addition, multiplication, and other mathematical operations.
Commonly used Number systems are, Positional Number System & Non positional Number System. The Roman Number System is an example of non-positional number system. Here we are going to discuss the positional Number system consisting of decimal, binary, octal and hexadecimal in detail. Also, we consider binary arithmetic of signed & unsigned numbers. We will be discussing various binary codes to represent the data.
Overview of the course:
Familiarize number representation in different number systems. The characteristics of Decimal, Binary, Octal and Hexadecimal number systems are discussed with specific remarks on the significance of radix (base) of a number system which provides the means of quantifying information for processing by digital systems. The representations of these numbers as integer as well as fractional parts are also discussed.
Next, we consider the Number base conversion techniques between Decimal to Binary, Octal and Hexadecimal systems, conversions of binary, octal and Hexadecimal numbers to Decimal, Binary to octal & Hexadecimal, Octal and Hexadecimal to Binary, Hexadecimal to Octal and Octal to hexadecimal conversions. Such conversions are very helpful in using a particular representation in some specific application.
The third module covers the binary arithmetic. First, we discuss addition, subtraction, multiplication and division of unsigned binary numbers, after that we will see the different representations of signed binary numbers & the binary arithmetic, concentrating more on One’s and Two’s complement representations and arithmetic.
The last module is dedicated for discussion on various binary codes to represent the data. They may consist of numerals, Alphabets or special characters. Mainly we study BCD, Gray code, Excess-3 code, ASCII code and their conversions to other codes. Some practical applications that demand such conversions are also mentioned. Error detection and correction techniques used while transmitting and receiving data in binary form to distant destinations are also discussed. Problem solving sessions are included for all relevant topics.