Every bit can be either 0 or 1. Therefore 4 bits can encode a maximum of 42 = 16 digits.
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Assuming the number holds an unsigned number, the range of numbers for 4 bits is 0-7. 7 is a prime number.
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A decimal digit requires 4 bits of memory space to represent all possible values. So N decimal digits will require 4N bits to store in decimal format. On the other hand, if the same N decimal digits were stored as a binary number, they should require log2(10N) bits, that is, about 3.32N bits. So storing the decimal representation uses about 20% more memory. To put it another way, 4 bits is capable of holding one of 16 different values. By using it to store decimal digits, it is only being used to hold one of 10 different values.
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