Question

"The binary pattern 01000001 represents the number 65." Write a brief response explaining whether you believe this statement is always true. Explain your reasoning.

Answer 1

Answer:

Yes

Explanation:

Yes this statement is always true.

Starting from right the first digit represents 1 and second digit represents 2 and so forth.

Starting from right the sequence becomes

1,2,4,8,16,32,62,128 for 8 binary digits

If 1 is written then we count it else for 0 we don't count it

for example 01 means 1 and 10 means 2 and 11 means 3 as 2+1=3

for 01000001 only place that is filled is for 1 and 64 therefore complete decimal digit shall be 64+1=65 and it would always remain same.

In subscript of 2 we can write  $2^{n}$, where n=0,1,2,3,4,...

For first digit from right $2^{n}$ will be $2^{0}$ which is 1. For second digit from right $2^{1}$ which will be 2 so on and so forth.

For this question we have $2^{0}$ and $2^{6}$ which will be 1+64=65