Question

Which of the following options completes the sentence: Grouping binary digits in groups of four makes converting to _______ easier?

a) Hexadecimal
b) Octal
c) Decimal
d) Binary

Answer 1

Grouping binary digits in fours simplifies the conversion to hexadecimal, each group of four binary digits corresponds to a single hexadecimal digit.

Therefore, the correct answer is: option a) Hexadecimal

Step-by-step explanation:

Hexadecimal numbers use base 16, and therefore only require one character for every four binary bits, which use base 2. The possible values of a four-bit binary sequence (0000 to 1111) correspond exactly to the hexadecimal digits (0 to F).

Grouping binary digits in groups of four makes converting to hexadecimal easier. This is because each group of four binary digits, also known as a nibble, can be directly mapped to a single hexadecimal digit.

For example, the binary sequence 1101 1010 when grouped into nibbles can be easily converted to the hexadecimal number DA. The first nibble (1101) converts to the hexadecimal digit D, and the second nibble (1010) converts to the hexadecimal digit A.