How many bits....How do I calculate this?


#1

I am new to this and I just don’t understand how to find these answers. I have looked for videos or other examples but I have not had any luck. I understand using the flippy do but this just doesn’t make sense

“What is the minimum number of bits you would need to encode the 26 letters of the alphabet plus a space - a total of 27 characters?”

“8 bits is enough to represent 256 different numbers. How many total bits do you need to represent 512 (twice as many) numbers?”


#2

I believe you’ll find the answers here: https://quizlet.com/254623830/computer-science-study-guide-u-1-3-flash-cards/

I’ll take a crack at the explanation…
When looking for the number of bits needed to represent a given number of characters (letters, numbers, or symbols), you need to look at the powers of 2. For example, the reason that 5 bits are required to represent 27 characters is that 2^2=4 (4 is not enough), 2^3 is 8 (still not enough)… 2^5 is 32. Since 32 > 27, at 2^5, or 5 bits, you now have enough unique permutations to represent all 27 characters.


#3

For both questions, it is helpful to know how many values you can represent with different quantities of bits. The flippy-do is 8 bits. You can count from 0-255 (or 00000000 to 11111111 in binary) so 256 different values. This formula may be helpful for you. It works with binary, decimal, hex or any number system:

So for the first question, how many bits do you need for the alphabet and a space? Or in other words, how many bits are needed to represent at least 27 values? Well, 4 bits can only give you 16 possible values. (2^4 = 15). 5 bits (2^5) gives you 32 unique values, which is enough unique values to hold the alphabet and a space. Answer is 5 bits.

The second question, you can do without needing math by knowing that every additional bit doubles the amount of values you can have. 8 bits, 2^8 = 256, as the problem says, and 2^9 = 512, so 9 bits would double the amount of values to 512.