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# Number Bases Trivia Quiz

### Data is stored in a computer as a series of zeros and ones. It is called the binary system. This is the lowest possible number base since there are only 2 digits. This quiz will introduce other bases and how they are used in programming.

A multiple-choice quiz by denmarks. Estimated time: 4 mins.

Author
Time
4 mins
Type
Multiple Choice
Quiz #
234,030
Updated
Dec 03 21
# Qns
10
Difficulty
Average
Avg Score
7 / 10
Plays
1753
Last 3 plays: Guest 197 (4/10), Guest 105 (4/10), Guest 94 (7/10).
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Question 1 of 10
1. A number base is the method we use to display and process numbers. Since we have 10 fingers we probably developed our number system based on 10 different digits. What digits are used in the octal system? Octal means eight. Hint

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Question 2 of 10
2. Since there are only 10 different digits, we can't have any base greater than 10.

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Question 3 of 10
3. Each position to the left of the decimal point has a base value equal to the base raised to the position where the first position is zero. In decimal it would be 10^0=1; 10^1=10; 10^2=100; etc. What would 100 in hexadecimal (base 16) be in decimal? Hint

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Question 4 of 10
4. While traveling to another planet, you see on the blackboard the math problem 13 + 15 = 31. What base are they using? Looks like there is a carry. Hint

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Question 5 of 10
5. On another planet you see 15 - 7 = 7. What base are they using? Hint

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Question 6 of 10
6. A core dump is used for debugging a program. Rather than print in binary, the hexadecimal system is used. It is very easy to convert between the systems by just converting each hex digit to binary and placing the results next to each other. What would be the binary value of hex FE? I always show binary in groups of 4 digits for ease of reading. Hint

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Question 7 of 10
7. What would be the decimal value of 1111 1110? Hint

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Question 8 of 10
8. In a core dump you would show the address at the left. If the highest computer address was 65535, how many hexadecimal positions would you need to display it? Hint

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Question 9 of 10
9. To convert an octal number to hexadecimal, just multiply by 2 and add 16.

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Question 10 of 10
10. The following math problem uses 4 different number bases less than 10. 23+25+35=70. What is the problem in decimal? Hint

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Quiz Answer Key and Fun Facts
1. A number base is the method we use to display and process numbers. Since we have 10 fingers we probably developed our number system based on 10 different digits. What digits are used in the octal system? Octal means eight.

There are always the same number of digits as the base name implies. Since we always use zero, the highest digit is one less than the base name.
2. Since there are only 10 different digits, we can't have any base greater than 10.

There is no limit to the base. We just have to invent new digits. In the hexahecimal (base 16) system we use 0-9 and A-F.
3. Each position to the left of the decimal point has a base value equal to the base raised to the position where the first position is zero. In decimal it would be 10^0=1; 10^1=10; 10^2=100; etc. What would 100 in hexadecimal (base 16) be in decimal?

Since it is in the third position and there is a 1 the value is 1*16^2.
4. While traveling to another planet, you see on the blackboard the math problem 13 + 15 = 31. What base are they using? Looks like there is a carry.

When you look at the problem you can see that 3 + 5 caused a carry. Therefore 3 + 5 is 1 greater than the base. Since in 3 + 5 in any base is equal to 8 in decimal and 8 is 1 greater than 7, the base is 7. 3 + 5 = 11 carry the 1. 1 + 1 + 1 = 3. Result 31. In decimal 10 + 12 = 22.
5. On another planet you see 15 - 7 = 7. What base are they using?

Since 7 is greater than 5 we have to borrow from the next column. So X + 5 - 7 = 7. Therefore X must be 9 (decimal). When we borrow that is the base.
6. A core dump is used for debugging a program. Rather than print in binary, the hexadecimal system is used. It is very easy to convert between the systems by just converting each hex digit to binary and placing the results next to each other. What would be the binary value of hex FE? I always show binary in groups of 4 digits for ease of reading.

Just do conversions in groups of 4 binary digits. F = 1111 and E = 1110.
7. What would be the decimal value of 1111 1110?

128+64+32+16+8+4+2+0=254.
8. In a core dump you would show the address at the left. If the highest computer address was 65535, how many hexadecimal positions would you need to display it?

15*4096+15*256+15*16+15=65535. In hex it is FFFF.
9. To convert an octal number to hexadecimal, just multiply by 2 and add 16.