Brilliant Binary! Trivia Quiz

Answer: 1529m

The binary number system is used by computers and other electrical devices. It is nothing particularly special; it is just one type of numerical system. Our decimal system is in base ten, binary is in base two. This means that each place value in our system is the next power of ten in the sequence. In binary, each place value is the next power of two. With the decimal system the place values are as follows:

1 (10^0)
10 (10^1)
100 (10^2)
1,000 (10^3) etc.

With the binary system, the place values are as follows:

1 (2^0)
2 (2^1)
4 (2^2)
8 (2^3)

Now, here is where a piece of paper is very useful. Our number is 10111111001, so that means that we have the following:

1,024s:1
512s:0
256s:1
128s:1
64s:1
32s:1
16s:1
8s:1
4s:0
2s:0
1s:1

1,024 + 256 + 128 + 64 + 32 + 16 + 8 + 1 = 1,529

Answer: 100111010000

Anybody who is playing the quiz normally may ignore this, as it is repeated throughout the quiz, otherwise proceed into comprehension:

START:
The binary number system is used by computers and other electrical devices. It is nothing particularly special; it is just one type of numerical system. Our decimal system is in base ten, binary is in base two. This means that each place value in our system is the next power of ten in the sequence. In binary, each place value is the next power of two. With the decimal system the place values are as follows:

1 (10^0)
10 (10^1)
100 (10^2)
1,000 (10^3) etc.

With the binary system, the place values are as follows:

1 (2^0)
2 (2^1)
4 (2^2)
8 (2^3)
END.

To work this out, process of elimination is required, but it is not difficult. We know that we have a 12 bit (a bit is a digit) binary number. We can tell this as 2,048 is the place value for the 12th bit (2^11). The place value for the thirteenth bit is 4,096 (2^12), and this is too big. We need 1 lot of 2,048, but 0 lots of 1,024, as 2,048 + 1,024 = 3,072, which is too big. 2,048 + 512 = 2,560, which is too big as well, therefore we need 0 lots of 512. We need 1 lot of 256, as 2,048 + 256 = 2,304, which needs to be increased. Therefore we need 1 lot of 128, as 2,304 + 128 = 2,432. This still needs increasing, so we need 1 lot of 64, as 2,432 + 64 = 2,496. This needs increasing, but we need 0 lots of 32, as 2,496 + 32 = 2,528. This is too big, but 2,496 + 16 = 2,512, which is perfect. Therefore we need 0 lots of 8, 0 lots of 4, 0 lots of 2 and 0 lots of 1. So the number is 100111010000.

Answer: 11001100111

Anybody who is playing the quiz normally may ignore this, as it is repeated throughout the quiz, otherwise proceed into comprehension:

START:
The binary number system is used by computers and other electrical devices. It is nothing particularly special; it is just one type of numerical system. Our decimal system is in base ten, binary is in base two. This means that each place value in our system is the next power of ten in the sequence. In binary, each place value is the next power of two. With the decimal system the place values are as follows:

1 (10^0)
10 (10^1)
100 (10^2)
1,000 (10^3) etc.

With the binary system, the place values are as follows:

1 (2^0)
2 (2^1)
4 (2^2)
8 (2^3)
END.

This will take a long time, but is not particularly complicated. Firstly, we must work out what 1110111101 is in the decimal, or base ten system. We have:

512s:1
256s:1
128s:1
64s:0
32s:1
16s:1
8s:1
4s:1
2s:0
1s:1

512 + 256 + 128 + 32 + 16 + 8 + 4 + 1 = 957.

Then we need to work out what 1010101010 is in the decimal, or base ten system. We have:

512s:1
256s:0
128s:1
64s:0
32s:1
16s:0
8s:1
4s:0
2s:1
1s:0

512 + 128 + 32 + 8 + 2 = 682

Now, 957 + 682 = 1639, so this is the number which we need to convert into binary.

Now, we have an 11 bit (11 digit) number. We can tell this as the place value for the twelfth bit is 2,048 (2^11), which is too big and the place value for the 11th bit 1,024 (2^10). This needs increasing, but is not too big. We need 1 lot of 512, as 1,024 + 512 = 1,536. This still needs increasing, but we need 0 lots of 256, as 1,536 + 256 = 1,792, which is too big. As is 1,536 + 128, which equals 1,664, so we need 0 lots of 128. We need 1 lot of 64 and 1 lot of 32 as 1,536 + 64 = 1,600 and 1,600 + 32 = 1,632. We need 0 lots of 16 and 0 lots of 8 as 1,632 + 16 = 1,648 and 1,632 + 8 = 1,640. Both of these are too big. However, we need 1 lot os 4, 1 lot of 2 and 1 lot of 1 as 1,632 + 4 = 1,636, 1,636 + 2 = 1,638 and 1,638 + 1 = 1,639. Therefore our answer is 11001100111.

Answer: 1729

Anybody who is playing the quiz normally may ignore this, as it is repeated throughout the quiz, otherwise proceed into comprehension:

START:
The binary number system is used by computers and other electrical devices. It is nothing particularly special; it is just one type of numerical system. Our decimal system is in base ten, binary is in base two. This means that each place value in our system is the next power of ten in the sequence. In binary, each place value is the next power of two. With the decimal system the place values are as follows:

1 (10^0)
10 (10^1)
100 (10^2)
1,000 (10^3) etc.

With the binary system, the place values are as follows:

1 (2^0)
2 (2^1)
4 (2^2)
8 (2^3)
END.

Firstly, we need to convert our numbers into the decimal, or base ten system. Our first number is 1110001110. This means that we have:

512s:1
256s:1
128s:1
64s:0
32s:0
16s:0
8s:1
4s:1
2s:1
1s:0

512 + 256 + 128 + 8 + 4 + 2 = 910.

Then we have to convert our second number which is 1100110011. This means that we have:

512s:1
256s:1
128s:0
64s:0
32s:1
16s:1
8s:0
4s:0
2s:1
1s:1

512 + 256 + 32 + 16 + 2 + 1 = 819.

910 + 819 = 1,729, so that is our answer.

Answer: 10011

Anybody who is playing the quiz normally may ignore this, as it is repeated throughout the quiz, otherwise proceed into comprehension:

START:
The binary number system is used by computers and other electrical devices. It is nothing particularly special; it is just one type of numerical system. Our decimal system is in base ten, binary is in base two. This means that each place value in our system is the next power of ten in the sequence. In binary, each place value is the next power of two. With the decimal system the place values are as follows:

1 (10^0)
10 (10^1)
100 (10^2)
1,000 (10^3) etc.

With the binary system, the place values are as follows:

1 (2^0)
2 (2^1)
4 (2^2)
8 (2^3)
END.

Firstly, we need to convert the binary numbers into decimal, or base ten numbers. Our first number is 11111101, so we have:

128s:1
64s:1
32s:1
16s:1
8s:1
4s:1
2s:0
1s:1

128 + 64 + 32 + 16 + 8 + 4 + 1 = 253.

Our second number is 11101010, so we have:

128s:1
64s:1
32s:1
16s:0
8s:1
4s:0
2s:1
1s:0

128 + 64 + 32 + 8 + 2 = 234.

253 - 234 = 19.

Now we have our answer, we need to convert it into binary. We know that it is a 5 bit (5 digit) binary number as the place value for the sixth bit is 32 (2^5), which is too big. The place value for the fifth bit, however, is 16 (2^4), which is the next lowest and is not too big. It is too small, however, so we have 1 lot of 16 and we need to add something. However, we have 0 lots of 8, as 16 + 8 = 24, which is too big. We have 0 lots of 4 too, as 16 + 4 = 20, which is too big as well. Therefore we have 1 lot of 2 and 1 lot of 1, as 16 + 2 = 18 and 18 + 1 = 19, which is perfect.

Answer: 11

Anybody who is playing the quiz normally may ignore this, as it is repeated throughout the quiz, otherwise proceed into comprehension:

START:
The binary number system is used by computers and other electrical devices. It is nothing particularly special; it is just one type of numerical system. Our decimal system is in base ten, binary is in base two. This means that each place value in our system is the next power of ten in the sequence. In binary, each place value is the next power of two. With the decimal system the place values are as follows:

1 (10^0)
10 (10^1)
100 (10^2)
1,000 (10^3) etc.

With the binary system, the place values are as follows:

1 (2^0)
2 (2^1)
4 (2^2)
8 (2^3)
END.

Firstly, we should convert into the decimal, or base ten system. Our first number is 11100101, so we have:

128s:1
64s:1
32s:1
16s:0
8s:0
4s:1
2s:0
1s:1

128 + 64 + 32 + 4 + 1 = 229.

Our second number is 11011010, so we have:

128s:1
64s:1
32s:0
16s:1
8s:1
4s:0
2s:1
1s:0

128 + 64 + 16 + 8 + 2 = 218.

229 - 218 = 11.

Answer: 1111

Anybody who is playing the quiz normally may ignore this, as it is repeated throughout the quiz, otherwise proceed into comprehension:

START:
The binary number system is used by computers and other electrical devices. It is nothing particularly special; it is just one type of numerical system. Our decimal system is in base ten, binary is in base two. This means that each place value in our system is the next power of ten in the sequence. In binary, each place value is the next power of two. With the decimal system the place values are as follows:

1 (10^0)
10 (10^1)
100 (10^2)
1,000 (10^3) etc.

With the binary system, the place values are as follows:

1 (2^0)
2 (2^1)
4 (2^2)
8 (2^3)
END.

Our first job is to convert our numbers into decimal, or base ten numbers. Our first number is 101, so we have:

4s:1
2s:0
1s:1

4 + 1 = 5.

Our second number is 11, so we have:

2s:1
1s:1

2 + 1 = 3.

5 x 3 = 15.

Now that we have our answer, we must convert it into binary. We know that it cannot be a 5 bit (5 digit) binary number, as the place value for the fifth bit is 16 (2^4), which is too big. Therefore, we must have a four bit binary number, as the place value for the fourth but is 8 (2^3), which is not too big. It is, however, too small, so we have 1 lot of 8 and 1 lot of 4, as 8 + 4 = 12. This draws us closer to our target of 15, but we are not quite there, so we have 1 lot of 2, as 12 + 2 = 14. We are still a little way of, so we have 1 lot of 1, as 14 + 1 = 15, which is perfect. Therefore our number is 1111.

Answer: 90

Anybody who is playing the quiz normally may ignore this, as it is repeated throughout the quiz, otherwise proceed into comprehension:

START:
The binary number system is used by computers and other electrical devices. It is nothing particularly special; it is just one type of numerical system. Our decimal system is in base ten, binary is in base two. This means that each place value in our system is the next power of ten in the sequence. In binary, each place value is the next power of two. With the decimal system the place values are as follows:

1 (10^0)
10 (10^1)
100 (10^2)
1,000 (10^3) etc.

With the binary system, the place values are as follows:

1 (2^0)
2 (2^1)
4 (2^2)
8 (2^3)
END.

First of all, we have to convert our binary numbers to base ten, or decimal numbers. Our first number is 1001, so we have:

8s:1
4s:0
2s:0
1s:1

8 + 1 = 9.

Our second number is 1010, so we have:

8s:1
4s:0
2s:1
1s:0

8 + 2 = 10.

9 x 10 = 90, so that's our answer.

Answer: 10101111

Anybody who is playing the quiz normally may ignore this, as it is repeated throughout the quiz, otherwise proceed into comprehension:

START:
The binary number system is used by computers and other electrical devices. It is nothing particularly special; it is just one type of numerical system. Our decimal system is in base ten, binary is in base two. This means that each place value in our system is the next power of ten in the sequence. In binary, each place value is the next power of two. With the decimal system the place values are as follows:

1 (10^0)
10 (10^1)
100 (10^2)
1,000 (10^3) etc.

With the binary system, the place values are as follows:

1 (2^0)
2 (2^1)
4 (2^2)
8 (2^3)
END.

For our first division question, we must begin by converting our binary numbers into decimal, or base ten numbers. Our first number is 1010111100, so we have:

512s:1
256s:0
128s:1
64s:0
32s:1
16s:1
8s:1
4s:1
2s:0
1s:0

512 + 128 + 32 + 16 + 8 + 4 = 700.

Our second number is 100, so we have:

4s:1
2s:0
1s:0

4 + 0 + 0 = 4.

700 divided by 4 = 175.

Now that we have our answer, we must convert it into a binary number. We know that it is an eight bit (eight digit) binary number as the place value for the ninth bit is 256 (2^8), which is too big. The next lowest one is the place value for the eighth bit, which is 128 (2^7), which is not too big. It is too small, however, so we have to increase it. We have 1 lot of 128, but 0 lots of 64, as 128 + 64 = 192, which is too big. We do have 1 lot of 32, however, as 128 + 32 = 160. This is still too small, but regardless, we have 0 lots of 16, as 160 + 16 = 176, which is too big. Therefore, we have 1 lot of 8, 1 lot of 4, 1 lot of 2 and 1 lot of 1. This is because 160 + 8 = 168, 168 + 4 = 172, 172 + 2 = 174 and 174 + 1 = 175. This is perfect, so our number is 10101111.

Answer: Two

Anybody who is playing the quiz normally may ignore this, as it is repeated throughout the quiz, otherwise proceed into comprehension:

START:
The binary number system is used by computers and other electrical devices. It is nothing particularly special; it is just one type of numerical system. Our decimal system is in base ten, binary is in base two. This means that each place value in our system is the next power of ten in the sequence. In binary, each place value is the next power of two. With the decimal system the place values are as follows:

1 (10^0)
10 (10^1)
100 (10^2)
1,000 (10^3) etc.

With the binary system, the place values are as follows:

1 (2^0)
2 (2^1)
4 (2^2)
8 (2^3)
END.

The first thing which we have to do is convert our numbers from binary to decimal, or base ten. Our first number is 10000, so we have:

16s:1
8s:0
4s:0
2s:0
1s:0

16 + 0 + 0 + 0 + 0 = 16.

Our second number is 1000, so we have:

8s:1
4s:0
2s:0
1s:0

8 + 0 + 0 + 0 = 8.

16 divided by 8 = 2.