Let’s reinforce what we learned in the previous exercise by practicing our counting to eight in binary. Eight may seem like a random number to stop at, but check out the table below and try to pick up the pattern of the counting.

Decimal | Binary |
---|---|

0 | 0 |

1 | 1 |

2 | 10 |

3 | 11 |

4 | 100 |

5 | 101 |

6 | 110 |

7 | 111 |

8 | 1000 |

Each time we reach a power of two we have to add another digit. For example, when we reach the number `2`

or 2^{1}, the binary value goes from `1`

to `10`

.

Similarly, when we reach decimal `4`

(2^{2}), in binary we go from `11`

to `100`

. This pattern continues for all the powers of 2 (0, 2, 4, 8, 16, 32, 64, 128, etc).

In fact, this brings us to our first trick to figuring out a number in binary. The highest a binary number can be is **2 ^{n} - 1**, where

`n`

is the number of digits in the binary number.`011010001010`

is 12 digits long; therefore, the highest number that can be represented in binary with these digits is `4095`

:

2^{12} - 1 = 4095

If we changed all the digits of our 12-digit binary number to `1`

s, we get `4095`

in decimal.

111111111111 = 4095

Our next trick you may have picked up yourself. You will notice that all odd numbers in binary end in `1`

and all even numbers end in `0`

. This is a quick way to double-check your work.

### Instructions

**1.**

Create a variable called `answer1`

and set it equal to the highest numerical value that can be represented in a 13-bit binary number, eg `1111111111111`

.

**2.**

Now let’s try two more!
Create two more variables called `answer2a`

and `answer2b`

and set them equal to the highest numerical value that can be represented in a 5-bit binary number and a 15-bit number respectively.

**3.**

Finally, create two more variables, `answer3a`

and `answer3b`

. Set `answer3a`

equal to the MSB and `answer3b`

to the LSB of the binary number `011100100011`

.