论文标题
两者补充数字系统的斐波那契类似物
A Fibonacci analogue of the two's complement numeration system
论文作者
论文摘要
使用经典二人物的补充符号表示法，加法，减法和乘法的基本算术操作与未签名的二进制数字相同。我们介绍了两者补充符号的斐波那酸等效，我们表明该计数系统中的添加可以由确定性的有限状态传感器执行。结果是基于Berstel Adder，该加法器的添加了非阴性整数的通常的斐波那契表示，我们为此提供了新的建设性证明。此外，我们将两者补充符号的斐波那酸等效性描述为$ \ mathbb {z} $与特定语言之间的越来越多。
Using the classic two's complement notation of signed integers, the fundamental arithmetic operations of addition, subtraction, and multiplication are identical to those for unsigned binary numbers. We introduce a Fibonacci-equivalent of the two's complement notation and we show that addition in this numeration system can be performed by a deterministic finite-state transducer. The result is based on the Berstel adder, which performs addition of the usual Fibonacci representations of nonnegative integers and for which we provide a new constructive proof. Moreover, we characterize the Fibonacci-equivalent of the two's complement notation as an increasing bijection between $\mathbb{Z}$ and a particular language.
