Binary Number System

Binary Number System: Representations

Unfortunately, it is difficult to look at hundreds of zeroes and ones and have them make any sense. They all seem to blend into one another unless we can organize them in some useful way. The most common way to organize bits is by grouping them into 4-bit chunks known as "half-bytes" or "nybbles". Then, each of those 16 possible patterns of 0/1 are represented by a hexadecimal digit in the range of 0-F, as shown in the table.

By using the hexadecimal system, it is easy to write long strings of bits in a compact form. For example,

110101110010101011010010110101100011010111111

simply causes one's eyes to water. But let's break it up into 4-bit chunks, starting from the rightmost bit:

   1 1010 1110 0101 0101 1010 0101 1010 1100 0110 1011 1111

Notice that there are not enough bits for the leftmost group to be complete. We will simply pad it with some extra zeroes:

0001 1010 1110 0101 0101 1010 0101 1010 1100 0110 1011 1111

Next, we determine the hex digit for each of the groups:

0001 1010 1110 0101 0101 1010 0101 1010 1100 0110 1011 1111

 1 A E 5 5 A 5 A C 6 B F

Thus, the binary string 110101110010101011010010110101100011010111111 is equivalent to the hexadecimal string 1AE55A5AC6BF.

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