Binary Numbers?

Question

Help. I'm taking a computer course and there is one question about binary numbers I can' t get: Q: The binary number 11 would have a decimal equivalent of: Possible answers are: a) 2. b) 3. c) 5. d) 11. I want to say d, but is seems a little too obvious. Can someone please help????

Answer 1

B) 3

The binary numeral system, or base-2 number system, is a numeral system that represents numeric values using two symbols, 0 and 1.

Each place value increases so the first spot is worth 1. Then 2. Then 4. Then 8. Etc.

If you have 11, that is like have 1+2=3.

If you have 111, that is like having 1+2+4=7

If you have 1111, that is like having 1+2+4+8 =15

If you have 1001, that is like having 1+0+0+8 =9

If you have a calculator and can switch between BIN and DEC, you can figure these out effortlessly. BIN stands for Binary and is the base-2 system. DEC stands for Decimal and is the base-10 system that we always use.

Here is the equivalent of numbers 0-10 in Binary:
0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010

Answer 2

The answer is three because 1*2^1+1*2^0=3

Start from the right, if there's a 1, that digit will be 1*2^0, otherwise, it's 0*2^0, as you move to the left, add one to your exponent and continue, multiplying it by either one or zero, add them all up and you have your answer. When you get used to it, you can drop the 1 or zero. If you have a one, use 2^n and leave the zero's out.

So, if you have 1010, it would be 2^3+2^1=10