Translate BCD to pure binary: Given the BCD-coded sequence 0111 1001 0011 (which represents decimal digits 7, 9, and 3), what is the equivalent binary bit string written contiguously?

Introduction / Context:Binary-Coded Decimal (BCD) stores each decimal digit as an independent 4-bit group. Converting a BCD representation to “binary” may mean two things: (1) concatenating the BCD nibbles into a single bit string (still digit-wise coded), or (2) translating the decimal value into a single pure binary number. Many entry-level questions intend the first interpretation—writing the BCD groups without spaces. This item tests that understanding.

Given Data / Assumptions:

• BCD groups: 0111 (digit 7), 1001 (digit 9), 0011 (digit 3).
• “In binary” here means the contiguous bit string formed by these BCD nibbles.
• No request to compute the single pure-binary value of the decimal number 793.

Concept / Approach:In BCD, each decimal digit is independent: 0→0000, 1→0001, …, 7→0111, 8→1000, 9→1001. Therefore, 7→0111, 9→1001, 3→0011. The contiguous BCD representation is just the concatenation of these groups, typically shown with spaces for readability but equivalent without spaces.

Step-by-Step Solution:

Verification / Alternative check:If instead the problem asked for the pure binary of decimal 793, you would compute 793 = 512 + 256 + 16 + 8 + 1, yielding the 10-bit binary 1100011001. That is a different representation than BCD concatenation, which remains digit-wise.

Why Other Options Are Wrong:

Common Pitfalls:Confusing BCD concatenation with conversion to a single pure-binary integer; mixing nibble boundaries; or misremembering BCD codes for 8 and 9.

Final Answer:011110010011