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: This statement is not always true. It can represent another number when the byte size is different. If the byte size is 4, then it would represent two numbers, 64 and 1.

Answer 2

TRUE

Explanation:

The given binary expression is 01000001.

We convert to a decimal numeral to see if is actually 65.

`01000001_2=0*2^7+1*2^6+0*2^5+0*2^4+0*2^3+0*2^2+0*2^1+1*2^0`

Note that any number multiplied by zero is still 0.

This implies that:

`01000001_2=0+1*64+0+0+0+0+0+1*1`

`01000001_2=64+1`

`01000001_2=65`

Therefore the given binary pattern represents the number 65.