# 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={Harold M. Lucal}, journal={IRE Trans. Electron. Comput.}, year={1959}, volume={8}, pages={449-458} }

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…

## 33 Citations

### A review of mathematical methods for construction of Gray codes

- Computer Science
- 2022

The problem of construction of Gray codes using mathematical methods using the direct method via Hamiltonian graphs as well as an iterative method that can be computationally implemented have been analyzed and compared.

### Towards quantitative comparison of computer number systems

- Computer Science1981 IEEE 5th Symposium on Computer Arithmetic (ARITH)
- 1981

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.

### A Basis for the Quantitative Comparison of Computer Number Systems

- Computer ScienceIEEE Transactions on Computers
- 1983

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. In…

### Automated Dynamic Error Analysis Methods for Optimization of Computer Arithmetic Systems

- Computer Science
- 2015

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.

### Towards the Efficient Generation of Gray Codes in the Bitprobe Model

- Computer Science
- 2016

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.

### Space-Optimal Quasi-Gray Codes with Logarithmic Read Complexity

- Computer ScienceESA
- 2018

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.

### Integer Representation and Counting in the Bit Probe Model

- Computer Science, MathematicsAlgorithmica
- 2008

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.

### The Gray Code

- Computer ScienceJ. Univers. Comput. Sci.
- 2007

The properties and algorithms of the Gray code are summarised, and some interesting applications of the code are also treated.

### Signed Modified Reflected Binary Code

- Computer ScienceIEEE 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 defined…

## References

SHOWING 1-2 OF 2 REFERENCES

### The use of a reflected code in digital control systems

- Computer ScienceTrans. I R E Prof. Group Electron. Comput.
- 1954

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.

### Pulse code modulation

- BusinessTransactions of the American Institute of Electrical Engineers
- 1947

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 modulation…