countingprinciple下面是一个英文问题请用中文解答不然我会不明白的beforetheinventionofthetelephone,SamuelMorsedevelopedanefficientsystemforsendingmessagesasaseriesofdotsanddashes(shortorlongpulses).Intern

Question

counting principle
下面是一个英文问题
请用中文解答
不然我会不明白的
before the invention of the telephone,Samuel Morse developed an efficient system for sending messages as a series of dots and dashes
(short or long pulses).International code,a modified version of Morse code,is still widely used.
a).how many different characters can the internation code represent with one to four pulses?
b).how many pulses would be necessary to represent the 72 letters of the Cambodian alphabet using a system like Morse code?

Answer 1

题目大意：
在电话发明之前,莫斯创造了一种有效的消息传递系统,摩斯密码.（由长信号和短信号组成）
a)用1到4个信号能够代表多少不同的字符.
1个信号：或长或短,2个字符 2^1
2个信号：长短,长长,短长,短短=2^2=4
3个信号：2^3=8
4个信号：2^4=16
一共=2+4+8+16=30=2^(4+1)-2
b)要表示72个字符（72个柬埔寨字母）至少需要多少个信号?
设需要n个字符
有2^(n+1)-2>=72
2^(n+1)>=74
n+1>=log(2)74
n取最小整数
所以n+1=7
n=6