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Data Types and Data Storage
Published in Julio Sanchez, Maria P. Canton, Microcontroller Programming, 2018
Julio Sanchez, Maria P. Canton
Floating-point encodings are the most efficient format for storing numerical data in a digital device and binary arithmetic is the fastest way to perform numerical calculations. But other representations are also useful. BCD (binary-coded decimal) is a way of representing decimal digits in binary form. There are two common ways of encoding decimal digits in binary format. One is known as the packed BCD format and the other one as unpacked. In the unpacked format each BCD digit is stored in one byte. In packed form two BCD digits are encoded per byte. The unpacked BCD format does not use the four high-order bits of each byte, which is wasted storage space. On the other hand, the unpacked format facilitates conversions and arithmetic operations on some machines. Figure 3.9 shows the memory storage of a packed and unpacked BCD number.
Numeric Data in Memory
Published in Julio Sanchez, Maria P. Canton, Software Solutions for Engineers and Scientists, 2018
Julio Sanchez, Maria P. Canton
Binary floating-point encodings are usually considered the most efficient format for storing numerical data in a digital computer. Other representations are also used in computer work. Binary-coded decimal (BCD) is a representation of decimal digits in binary form. There are two common ways of storing BCD digits. One is known as the packed BCD format and the other one as unpacked. In the unpacked format one BCD digit is represented in one byte of memory storage. In packed form two BCD digits are encoded per byte of storage. The unpacked BCD format does not use the four high-order bits of each byte, which is wasted storage space. On the other hand, the unpacked format facilitates conversions and arithmetic operations on some machines. Figure 2.7 shows the memory storage of a packed and unpacked BCD number.
A tool for modeling systems
Published in William L. Chapman, A. Terry Bahill, A. Wayne Wymore, Engineering Modeling and Design, 2018
William L. Chapman, A. Terry Bahill, A. Wayne Wymore
7. Invalid BCD digit detector. In the Binary Coded Decimal (BCD) representation, each decimal digit is represented with four binary bits. The numbers 0 to 9 are represented by valid four-bit BCD digits, and the numbers 10 to 15 constitute invalid BCD digits. Assume the four bits are being transmitted on a serial line. Draw a state diagram for a single-input, single-output system that determines whether an invalid BCD digit has been received. If, at the end of the BCD word (the four bits), your system determines that the BCD digit is invalid, then its output should be 1 and remain 1 until another bit is received. The output should be 0 at all other times. Least-significant bits of the words appear first in time. You may ignore start-up transients; design your system for steady-state operation. You need not minimize your system. It will be easier if you treat the input as a sequence of words and not as a string of bits. That is, test bits 1,2,3, and 4, then bits 5,6,7, and 8; do not test bits 1, 2,3, and 4, then bits 2,3,4, and 5. Call this system Z7; specify Z7 = ( S Z 7 , IZ7j 0Z7, NZ7, R Z 7). If you wanted to test your model by applying all possible input trajectories and all reasonable initial states, how many test trajectories would you need and how long would they have to be?
An Efficient and Optimized Converter for Fast Binary to Decimal Conversion
Published in International Journal of Electronics Letters, 2022
Pavan Kalyan Kumar M, Bhaskara Rao Jammu, Sreehari Veeramachaneni, Noor Mahammad Sk
As the applications of decimal arithmetic in various fields of technology are getting increased day by day, the requirement for faster methods is also getting increased. One of the most vital operations among decimal arithmetic is multiplication; there are three ways to perform multiplications; they are, serial multiplication (Erle and Schulte, 2003; Erle et al., 2005), parallel (word-by-digit) multiplication (Erle et al., 2005; Han and Ko, 2013; Jaberipur and Kaivani, 2007; Jaberipur and Kaivani, 2009; Vazquez et al., 2010) and digit-by-digit multiplication (James et al., 2008; Nicoud, 1971). Among these, digit-by-digit multiplication is preferred due to its regular structure and it is more appropriate for pipeline computations (Ahmed et al., 2018). In Binary Coded Decimal (BCD) ‘digit-by-digit’ multiplication, the intermediate partial product converter is needed which converts the results from binary to BCD as shown in the dotted area of Figure 1.
Personal reflections on 50 years of scientific computing: 1967–2017
Published in International Journal of Parallel, Emergent and Distributed Systems, 2020
In 1969, after graduating from Evansville with majors in mathematics and psychology, I worked for another accounting firm (Wright, Griffin, and Davis, CPAs) in Ypsilanti, Michigan while a graduate student in mathematics at The University of Michigan. That work involved the niche IBM System 3, a machine with BCD (binary coded decimal) integer arithmetic, 32-bit words, a rotating disk, line printer, an assembler, and 96-column punched cards about 1/3 the size of IBM 80-column cards for I/O. I led a team (of mathematics graduate students, with no prior experience with computing) to design and build an interpreter called PROFIT (Periodic Reporting Of Financial Input Transactions) with functionality similar to ABLE, including a monitor and all the physical I/O device drivers. The input was on punched cards, the financial reports were printed, and the financial data was stored on a hard disk drive. The disk data structures involved binary trees, linked lists, and garbage collection, all created by students with no prior knowledge of any of these concepts. Years later, I was contacted about why PROFIT, rewritten in COBOL (which had become available for the System 3 by that time), might be running so much slower than the original assembly language version.
Image enhancement by the combination of multivalued logic and Savitzky–Golay filter
Published in International Journal of Electronics Letters, 2019
Sayantani Karmakar, Supriya Karmakar
Among other multi-valued logics (MVLs), quaternary logic is very promising. It uses relatively simple encoding/decoding scheme with binary logic because quaternary logic is a radix 4 logic and binary logic is a radix-2 logic where 4 = 22. Signals in quaternary logic world can be easily interfaced in the binary world. Like other multivalued logic, many other logical operations can be performed with fewer numbers of gate, operations, bus, circuit elements, etc. Conversion between binary data to binary coded decimal can be performed easily, whereas that is complicated for other multivalued logic. Because of good compatibility between quaternary logic and binary logic, the coding is relatively easy in quaternary logic.