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Number Systems, Conversions and Codes
Published in Dale Patrick, Stephen Fardo, Vigyan ‘Vigs’ Chandra, Electronic Digital System Fundamentals, 2020
Dale Patrick, Stephen Fardo, Vigyan ‘Vigs’ Chandra
Hexadecimal numbers are used in digital systems to process large numbers. The base of this system is 16. The largest value displayed at a specific place is 15, which is displayed by digits 0 through 9 and the letters A, B, C, D, E, and F. The place values from the left of the hexadecimal point are powers of 16. Conversion of a hexadecimal number to a decimal number is similar to the other conversion processes. The hexadecimal number is recorded and the place values or powers of the base are then positioned under each digit. The values are then multiplied to indicate discrete place values. Conversion of decimal to hexadecimal is achieved by repetitive division. The quotient is transferred for the next division step and the remainder is recorded. The combined remainders form the hexadecimal number. Conversion of a binary number to hexadecimal is achieved by dividing the number into groups of four digits starting at the hexadecimal point. Each binary group is then changed into an equivalent hexadecimal value.
Probability and making decisions
Published in Andrew Metcalfe, David Green, Tony Greenfield, Mahayaudin Mansor, Andrew Smith, Jonathan Tuke, Statistics in Engineering, 2019
Andrew Metcalfe, David Green, Tony Greenfield, Mahayaudin Mansor, Andrew Smith, Jonathan Tuke
Hexadecimal is a positional numeral system with a radix (or base) of 16. It uses 16 distinct symbols: 0, …, 9, A, B, C, D, E, F. A pseudo random number generator appears to generate these symbols independently and with equal probabilities. Write down the probabilities of the following events as fractions. The next symbol is 8.The next two symbols are 53.The next two symbols are identical (i.e. one of 00, 11, …, FF).The next three symbols are ACE (in that order).The next four symbols are 7, A, C, E in any order.
Digital Electronics
Published in Dale R. Patrick, Stephen W. Fardo, Electricity and Electronics Fundamentals, 2020
Dale R. Patrick, Stephen W. Fardo
The hexadecimal number system is used in digital systems to process large number values. The base of this system is 16, which means that the largest number used in a place is 15. Digits used by this system are the numbers 0-9 and the letters A-F The letters A-F are used to denote the digits 10-15, respectively. The place values to the left of the hexadecimal point are the powers of 16: 160 = 1, 161 = 16, 162 = 256, 163 = 4096, 164 = 65,536, and so on.
New theorems for inverting the functions of logic gates in digital circuits
Published in Journal of Control and Decision, 2022
The designers of the digital logic circuits typically adopt binary and hexadecimal notation systems to explain the operations of digital circuits. Usually, they also combine transistors with several electronic components whenever they intend to construct logic gates that can produce effective microprocessor-based systems (Electronics-tutorials, 2022). Unfortunately, designers inevitably face with several tradeoffs on how they will suitably reduce and simplify the complexity of operations and whenever electric signals flow through the circuits. Circuit designers must therefore establish that the digital circuits have simple and explicit diagrammatic illustrations. Studies point out that complexity in the design of digital circuits can distort the process of identifying, justifying and mitigating the existence of noise and other sources of interference in the logic circuits (Chang et al., 2017; Hasuo & Imamura, 1998).