Topic Cover In PDF - Decimal, binary, octal, hexadecimal number system and conversion, binary weighted& non-weighted codes & code conversion, signed numbers, 1s, 2s & 9s complement codes, Binary arithmetic
Unit 1 delves into the exciting world of digital logic design by establishing the foundation using number systems and codes. Mastering these concepts reveals the complex dance of 0s and 1s that drives modern technology.
Number Systems: We begin with the well-known decimal (base 10) system, which has ten unique digits. However, for digital circuitry, Binary (base 2) reigns supreme, represented by only 0 and 1, providing simplicity and efficiency. Need a more compact representation? Octal (base 8) with 8 digits and Hexadecimal (base 16) with 16 digits (letters A-F joining 0-9) help to bridge the binary-human readability divide. Understanding the conversion between these systems becomes critical.
Codes: Information in digital circuits thrives on codes, which are specialized representations that go beyond basic number systems. Binary Weighted Codes, such as BCD (Binary Coded Decimal), assign distinct weights to each place. Each digit has its own 4-bit representation. Non-weighted codes, such as Grey code, are used in rotary encoders to reduce bit-flipping during transitions, maintaining accuracy. Mastering code conversion between these types is critical.
Signed numbers have an important role in representing negative values. Common ways are 1's complement, which inverts all bits, and 2's complement, which adds 1 to the 1's complement. Both have advantages, with 2's complement being more appropriate for arithmetic operations. The 9's complement, where the digits sum up to 9 (excluding leading 0s), is used to detect errors.
Binary Arithmetic: Addition, subtraction, multiplication, and even division have binary counterparts. Addition is simple, however, subtraction requires borrowing. Multiplication requires shifting and adding, whereas division employs repeated subtraction or specialized algorithms.
Unit 1 builds the framework for further exploration. Understanding number systems, codes, and signed number representation prepares you to explore the logic gates and circuits that power the digital world. Remember, practice is essential! So get some numbers, convert, code, and calculate your way to mastery!
