Test on Binary and hexadecimal number systems

Question 1: The range of numbers that can be represented by an n-bit two's complement system is from -2^(n-1) to 2^(n-1) - 1.

A. Yes

B. No

Explanation: The study materials explicitly state: 'The range of numbers that can be represented by an n-bit two's complement system is from -2^(n-1) to 2^(n-1) - 1.'

Question 2: According to the study materials, which action is a common mistake when grouping bits for binary-to-octal or binary-to-hexadecimal conversions?

A. Forgetting to add 1 when calculating two's complement.

B. Incorrectly grouping bits from the left side of the binary number.

C. Miscalculating the power of the base for a given digit's position.

D. Assigning incorrect decimal values to hexadecimal letters.

Explanation: The study materials explicitly state under 'Common Mistakes and Misconceptions' that 'Incorrectly applying conversion rules: ... incorrectly grouping bits for binary-octal/hexadecimal conversions, are frequent mistakes. Ensure consistent grouping from the right.' This highlights grouping from the left as a common error. The other options are also common mistakes, but not the one specifically related to 'grouping bits' for these conversions as described.

Question 3: When converting an octal number to binary, each octal digit is converted into its four-bit binary equivalent.

A. Yes

B. No

Explanation: To convert an octal number to binary, each octal digit is converted into its three-bit binary equivalent, not four-bit.

Question 4: When converting from hexadecimal to binary, each hexadecimal digit is converted into its four-bit binary equivalent.

A. Yes

B. No

Explanation: To convert from hexadecimal to binary, each hexadecimal digit is individually converted into its corresponding four-bit binary equivalent, as stated in the study materials under 'Hexadecimal to Binary'.

Question 5: Which of the following represents the correct conversion of the hexadecimal number B2_16 to its decimal equivalent?

A. 178_10

B. 162_10

C. 176_10

D. 194_10

Explanation: To convert B2_16 to decimal, use the positional expansion formula. B corresponds to the decimal value 11. Therefore, B2_16 = B · 16^1 + 2 · 16^0 = 11 · 16 + 2 · 1 = 176 + 2 = 178_10.