exercise on binary number system


How do you write a binary number?

    Just as with decimal notation, we write a binary number as a string of symbols, but now each symbol is a 0 or a 1. To interpret a binary number, we multiply each digit by the power of associated with that 2 digit’s position. For example, consider the binary number 1101. This number is: 1 1 0 1= 3 2 10 12 12 0 2 12 31? +? +? +? =10 23 222120

What is the binary equivalent of 5?

    For example, the decimal number 5 is represented in the table as the binary number 0101. We could have represented the binary equivalent of 5 as 101, 00101, 0000000101, or with any other number of leading zeros. All answers are correct. Sometimes, though, you will be given the size of a storage location.

What is the answer to 15 + 1 in binary?

    The correct answer to the binary addition, 10000, requires five bits. But the computer (in our example) stores all integers in four bits. All bits beyond the rightmost four bits are discarded. So, the answer to 15 + 1 in binary on our 4 bit computer - would be zero (i.e., 0000).

Should binary numbers be represented in Base16 or hexadecimal?

    Fortunately, large binary numbers can be made much more compact—and hence easier to work with—if represented in base16, the so- called hexadecimal number system. You may wonder: Binary numbers - would also be more compact if represented in base-10—why not just convert them to decimal?
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