3. Digital Arithmetic - Part B
The chapter covers essential concepts of digital arithmetic, specifically focusing on BCD addition and subtraction using the excess-3 code, various binary multiplication methods, binary division techniques, and floating-point arithmetic. It illustrates the processes through numerous examples and details key algorithms like repeated left-shift and add, repeated add and right-shift for multiplication, and both repeated right-shift and subtract along with repeated subtract and left-shift algorithms for division. Additionally, the chapter discusses the operational characteristics of floating-point addition, subtraction, multiplication, and division.
Sections
Navigate through the learning materials and practice exercises.
What we have learnt
- Excess-3 code is an effective numeral system for BCD addition and subtraction.
- Binary multiplication can be performed using methods such as repeated left-shift and add, and repeated add and right-shift.
- Binary division can be executed via repeated right-shift and subtract or repeated subtract and left-shift methods, while floating-point arithmetic requires normalization to handle operations accurately.
Key Concepts
- -- Excess3 Code
- A non-weighted code used to express decimal numbers, where each digit is represented by its corresponding binary value plus 3.
- -- BCD (BinaryCoded Decimal)
- A class of binary encodings of decimal numbers where each decimal digit is represented by its own binary sequence.
- -- Binary Multiplication Algorithms
- Techniques for multiplying binary numbers, including the repeated left-shift and add method and the repeated add and right-shift method.
- -- FloatingPoint Arithmetic
- A method of representing real numbers that can accommodate a wide range of values by utilizing a format of mantissa and exponent.
Additional Learning Materials
Supplementary resources to enhance your learning experience.