Number Systems and Codes Questions

• Maximum single-digit value in BCD: For a single BCD digit, is the largest valid value equal to binary 1111 (decimal 15), or is the maximum decimal digit 9 represented as 1001?
• Nature of Gray code: Is Gray code an “octal (base-8) number system,” or is it a binary code in which only one bit changes between successive values to reduce transition errors?
• Number systems — converting decimal fractions to binary: Consider the specific case of converting a decimal fraction (the part to the right of the decimal point, such as 0.625) into its binary representation. Evaluate the statement: “A decimal fraction can be converted to binary by using the repeated division-by-2 method.”
• BCD encoding — check the claim for decimal 73: Binary-Coded Decimal (BCD) represents each decimal digit with its 4-bit binary code. Evaluate: “The BCD equivalent of 73 is 01001001.”
• Basic terminology — how many bits are in a byte? Confirm or refute the common statement: “A byte has 8 bits.” Provide reasoning relevant to modern digital systems and memory organization.
• Cross-base identity check — decimal 15 across binary, hex, and BCD: Validate the compound statement: “15₁₀ = 1111₂ = F₁₆ = 0001 0101 (BCD).”
• Context statement — role of digital circuitry: Evaluate the claim: “Digital circuitry is the foundation of digital computers and many automated control systems.” Give a brief justification rooted in system architecture.
• Hexadecimal digits — precise definition of symbols: Assess the statement: “The hexadecimal number system consists of 16 digits, 0–15.” Clarify what the digits actually are in base-16.
• Why hexadecimal is popular — primary advantage: Judge the statement: “The primary advantage of the hexadecimal numbering system is the ease of conversion to and from binary.”
• Decimal system digits — fact check: Evaluate the statement: “The decimal number system consists of the digits 0–10.”
• Octal-to-binary conversion rule — verify bit-grouping: Assess the statement: “Octal-to-binary conversion is accomplished by simply replacing each octal digit with its 4-bit binary equivalent.”
• Hex-to-binary identity — validate 3C1D₁₆: Confirm or refute: “3C1D₁₆ equals 1111 0000 0111 01₂” (i.e., 11110000011101₂ when spaces are removed).
• Computer architecture — “Word size” refers to the number of bits in the binary word that the digital system natively operates on (for example, 8-bit, 16-bit, 32-bit, 64-bit processors). Evaluate the statement.
• Software engineering — A “debugging utility” (debugger) is used to locate and remove bugs from a program. Evaluate this statement for accuracy.
• Signal representation — “A digital representation of an analog quantity is used in audio recording of music.” Evaluate the example.
• Hexadecimal in digital design — “Hex is commonly used as a shorthand to represent strings of bits.” Judge the statement.
• Octal number system — Confirm or refute: “The octal system consists of eight digits, 0 through 7.”
• Numeration for digital electronics — Evaluate: “Digital electronics must use a numbering system that has more than ten digits.”
• BCD vs. pure binary — “A Binary-Coded Decimal (BCD) representation of a given numeric value always requires more bits than its pure binary representation.” Evaluate.
• Place-value weighting — “Each position in a multi-digit decimal number has a weight equal to a power of 10 only.” Evaluate the claim.