Arithmetic Operations for Digital Computers Using a Modified Reflected Binary Code

@article{Lucal1959ArithmeticOF,
  title={Arithmetic Operations for Digital Computers Using a Modified Reflected Binary Code},
  author={H. Lucal},
  journal={IRE Trans. Electron. Comput.},
  year={1959},
  volume={8},
  pages={449-458}
}
  • H. Lucal
  • Published 1959
  • Computer Science
  • IRE Trans. Electron. Comput.
The reflected binary or Gray code has been used chiefly in analog-to-digital conversion devices because its code sequences, representing any two consecutive integral numbers, differ in only one digit. This paper presents a method for performing the arithmetic operations of addition, subtraction, multiplication, and division using a modified reflected binary code. The modification for integral numbers is essentially the addition of an even parity check bit to the Gray code representation. This… Expand
Towards quantitative comparison of computer number systems
  • S. Ong, D. Atkins
  • Computer Science
  • 1981 IEEE 5th Symposium on Computer Arithmetic (ARITH)
  • 1981
TLDR
An evolving Arithmetic Design System to support the quantitative evaluation of alternate number systems with respect to a given application and realization technology is described. Expand
A Basis for the Quantitative Comparison of Computer Number Systems
This paper describes aspects of an arithmetic design system (ADS) to support the quantitative evaluation of alternate number systems with respect to a given application and realization technology. InExpand
Automated Dynamic Error Analysis Methods for Optimization of Computer Arithmetic Systems
TLDR
Systems for the detection of floating point rounding errors are highly important and fast, efficient and easy to use implementations of these detection systems is a high priority. Expand
Number Systems and Arithmetic
TLDR
Overflows, underflows, scaling, and complement coding that characterize machine number systems are direct consequences of finitude and, in fact, illustrate both the detrimental and beneficial consequences ofFinitude. Expand
Towards the Efficient Generation of Gray Codes in the Bitprobe Model
TLDR
A data structure is given that disproves the conjecture that, when a space-optimal data structure uses only 1 bit write to perform these operations, then every bit in the data structure must be inspected in the worst case. Expand
Space-Optimal Quasi-Gray Codes with Logarithmic Read Complexity
TLDR
This paper presents construction of quasi-Gray codes of dimension n and length 3^n over the ternary alphabet with worst-case read complexity O(log n) and write complexity 2 and significantly improves on previously known constructions and breaks the Omega(n) worst- case barrier for space-optimal (non-redundant) quasi- Gray codes. Expand
Integer Representation and Counting in the Bit Probe Model
TLDR
This work examines the problem of integer representation in a nearly minimal number of bits so that the increment and the decrement operations can be performed using few bit inspections and fewer bit changes. Expand
The Gray Code
  • R. W. Doran
  • Computer Science
  • J. Univers. Comput. Sci.
  • 2007
TLDR
The properties and algorithms of the Gray code are summarised, and some interesting applications of the code are also treated. Expand
Signed Modified Reflected Binary Code
  • D. Agrawal
  • Mathematics, Computer Science
  • IEEE Transactions on Computers
  • 1976
A signed modified reflected binary (SMRB) code with unique representability of both positive and negative numbers has been proposed in this correspondence. The bit pattern in this code can be definedExpand
Addition and Subtraction
The addition of two binary numbers can be defined by the addition of two binary digits (a and b) and a carry digit (c) generated by the next less significant section, resulting in a sum digit (S) andExpand
...
1
2
3
...

References

SHOWING 1-2 OF 2 REFERENCES
The use of a reflected code in digital control systems
  • F. A. Foss
  • Computer Science
  • Trans. I R E Prof. Group Electron. Comput.
  • 1954
TLDR
This paper describes several designs of typical reflected binary switching circuits, which can be used as digital control elements in the described original types of digital positional servomechanisms and digital accumulators. Expand
Pulse code modulation
A radically new modulation technique for multichannel telephony has been developed which involves the conversion of speech waves into coded pulses. An 8-channel system employing pulse code modulationExpand