That Scary Binary System! Trivia Quiz

Answer: 0, 1

Only zero and one are used because they are the only numbers that, when placed in a binary number, will not multiply out to a higher place value. Example: 20 in binary system would equal (2^2 * 1) + (2^0 * 0) which is equal to 4. Four is a power of two, so it needs a new place value spot for itself.

Answer: odd

All powers of two except 2^0 are even. If you add even numbers together, they will always be even. If you have a one in the final spot, it literally translates as (2^0 * 1), which equals one. An odd number plus an even number will be an odd number. One is an odd number, and because every other power of two is even, you simply have to add an odd to make your binary number odd.

Answer: 127

The highest value you can have in each of the seven slots of your binary number is one, so you have 1111111 as your binary number. The number on the right is (2^0 * 1) and with each place value to the left of it, the exponent on two increases by one. Your expression translates to (2^6 * 1) + (2^5 * 1) + (2^4 * 1) + (2^3 * 1) + (2^2 * 1) + (2^1 * 1) + (2^0 * 1), which can be simplified to 64 + 32 + 16 + 8 + 4 + 2 + 1.

These numbers can be combined for a result of 127.

Answer: three

Remember, you find the value of each digit and add the values together. (2^1 * 1) + (2^0 * 1), which can be simplified to 2 + 1, which is equal to three.

Answer: 101

To determine how many numbers you will need, find out the greatest power of two 5 has equaled or surpassed in value. In this case, it is 2^2, which equals 4. 2^3 will not work because 5 has not yet equaled or surpassed eight in value. Insert a 1 into the 2^2 spot and see if you can insert a one into the 2^1 spot. 2^1 equals 2, and the sum of (2^2 * 1) + (2^1 * 1) is equal to six, which is greater than five. Place a zero in your 2^1 slot and check your 2^0 spot. (2^2 * 1) + (2^0 * 1) is equal to 4 + 1, which can be simplified to five.

Answer: eleven

You've got four numbers, so your equation would read (2^3 * 1) + (2^2 * 0) + (2^1 * 1) + (2^0 * 1), which equals 8 + 0 + 2 + 1, which can be simplified to 11.

Answer: 1110

First, find out what power of two fourteen has equaled or surpassed in value. Looking closer, we see that 2^3, which is eight, is the highest power 14 has surpassed. Put a 1 in your first spot, and look to your next power, 2^2. 8 + 4 is 12, which is less than 14, so put another 1 there. Look to 2^1, which is 2, and add it to your 12, which makes 14. Since you have your number, you may think you're done, but you can't leave your 2^0 slot open, so why don't we stick a zero there. Your final answer is 1110.

Answer: fifty-three

Count the number of numbers in the equation, and you see there are six of them. Therefore, your first power is 2^5 (don't forget the right-hand number is to the zero power!). Your equation is (2^5 * 1) + (2^4 * 1) + (2^3 * 0) + (2^2 * 1) + (2^1 * 0) + (2^0 * 1), which can be simplified to 32 + 16 + 0 + 4 + 0 + 1. Add your numbers up, and you get 53.

Answer: 100101

Seeing what power thirty-seven has surpassed, we discover that 2^5 is thirty-two, just what we're looking for. Stick a 1 in your first slot, and progress to the 2^4 slot. 2^4 equals 16, and when added to 32, makes 48, which is greater than 37. Stick a zero in the next slot. 2^3 equals eight, which, added to 32, makes 40, which is also greater than 37. Put another zero. Your next power is 2^2, which is 4. Add it to 32 to get 36, which is less than 37. Put a one in your next slot. 2^1 equals 2, which, when added to 36, will result in the number 38.

Unfortunately, this makes your number equal to 38, which is greater than 37. Put a zero here and progress to your final slot, 2^0. 2^0 equals one, and 36 + 1 equals 37. Congratulations! Stick a one here, and get the final answer 100101.

Answer: 1365

Eleven spots means eleven powers of two. Yup, you have to evaluate every power of two, from 0 to ten. Your long equation will read (2^10 * 1) + (2^9 * 0) + (2^8 * 1) + (2^7 * 0) + (2^6 * 1) + (2^5 * 0) + (2^4 * 1) + (2^3 * 0) + (2^2 * 1) + (2^1 * 0) + (2^0 * 1), which can be simplified to 1024 + 0 + 256 + 0 + 64 + 0 + 16 + 0 + 4 + 0 + 1. Add these eleven numbers up to get 1365.

I hope you have done well on this quiz and learned a bit about the binary system!