云算法之Logarithms and Bits

最新推荐文章于 2025-03-30 05:59:51 发布

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本文讨论了如何确定计算机字长以表示从0到2的i次方加减1的任意数字。通过增加位数，可以扩大可表示的数字范围。例如，两个二进制位能表示0到3，而增加一位则能将表示范围扩展到0到7。每添加一位，可表示的数字数量翻倍。若要表示2的n次方，需要n位二进制数。

Bit:Binary digit（二进制数）位的缩写

Q：Suppose i want to build a new computer and i want to represent any number from 0 to 2 to the i plus minus 1 in my word length (字长) of my computer, and i want to represent any number from 0 to 2 to the i plus minus 1 in my word length of my computer. How many bits do i need to represent the number as big as two to the i plus one.

A：

1. What happens when you add one bit, what's the biggest number in binary you can represent in two bits. IT'S THREE. What is the biggest number i can represent when i add one more bit that goes from three to seven.

2.There are a total of four numbers i can represent with two bits. When i add another bit i double the number of numbers i can represent. If i want to represent two to the n ,how many bits do i need. One bit gave me two numbers.[ ]