You have got the math totally wrong. Here’s how it really is
since each bit can only take on either of two states only(1 and 0) , n bits as a whole can represents 2^n different quantities not numbers. When dealing with integers a standard short integer size of 2 bytes can represent 2^n – 1 (n=16 so 65535)which are mapped to decimal numbers in real life for compuational simplicity.
When dealing with 2 character they are two seperate entities (string is an array of characters). There are many ways to read the two characters on a whole, if you read is at as a string then it would be same as two seperate characters side by side. let me give you an example :
remember i will be using hexadecimal notation for simplicity!
if you have doubt mapping ASCII characters to hex take a look at this ascii to hex
for simplicity let us assume the characters stored in two adjacent positions are both A.
Now hex code for A is 0x41 so the memory would look like
1 byte ……. 2nd byte
01000100 01000001
if you were to read this from the memory as a string and print it out then the output would be
AA
if you were to read the whole 2 bytes as an integer then this would represent
0 * 2^15 + 1 * 2^14 + 0 * 2^13 + 0 * 2^12 + 0 * 2^11 + 1 * 2^10 + 0 * 2^9 + 0 * 2^8 + 0 * 2^7 + 1 * 2^6 + 0 * 2^5 + 0 * 2^4 + 0 * 2^3 + 0 * 2^2 + 0 * 2^1 + 1 * 2^0
= 17537
if unsigned integers were used then the 2 bytes of data would me mapped to integers between
0 and 65535 but if the same represented a signed value then then , though the range remains the same the biggest positive number that can be represented would be 32767. the values would lie between -32768 and 32767 this is because all of the 2 bytes cannot be used and the highest order bit is left to determine the sign. 1 represents negative and 2 represents positive.
You must also note that type conversion (two characters read as single integer) might not always give you the desired results , especially when you narrow the range. (example a doble precision float is converted to an integer.)
For more on that see this answer double to int
hope this helps.
solved How numbers are stored? [closed]