53. Fortunately, Jack Blake had done his English essay the night before and left early that morning. Jack lives 2,512m from school, how far is that in binary?
From Quiz Brilliant Binary!
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.
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