In binary number system "1" & "0" are used to represent the two different voltage levels or logic levels in digital circuits. However, in most applications, a long string of 1’s and 0’s occur, and makes the data presentation “nasty”. To condense this long string of 1’s and 0’s, the ___________ number system is (are) also used.

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BlackTom AI · Accepted Answer

The question discusses ways to condense long binary strings by using alternative number systems in digital data presentation.
Option a: decimal. While decimal is the standard base for everyday numbers, it is not typically used to condense binary data into compact representations because each decimal digit can carry about 3.32 bits of information, making the mapping less compact than other bases. However, there are contexts (such as representing the value of a binary string in decimal form or using decimal-based encodings like BCD) where binary information is shown in decimal digits, so decimal can play a role in presenting binary data, albeit not as a compact encoding.
Option b: octal. Octal uses 3-bit groups, which makes it a natural and compact way to represent binary data, especially in older systems and certain Unix-like environments. Each octal digit corresponds to exactly 3 binary bits, so long binary strings are condensed efficiently.
Option c: hexadecimal. Hexadecimal uses 4-bit groups, providing a highly compact representation for binary data. It is widely adopted in computing because it reduces long binary strings to a shorter form with each hex digit representing 4 bits, improving readability and ease of conversion.
Option d: all of the options. Given that each of the bases has a role in presenting or encoding binary information in some contexts—octal for 3-bit grouping, hexadecimal for 4-bit grouping, and decimal being used to display or encode data in decimal form in certain schemes—the statement that all of the options are used to condense binary data reflects the idea that multiple bases can be employed depending on the specific presentation goal or historical/technical context. While decimal is less about compact condensation than octal or hex, it can still be involved in displaying or encoding binary-derived values in decimal form, which supports the notion that all options have at least some relevance in various applications.

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