Questions: Module 5 Test Review Question 13 of 16 (1 point) Question Attempt: 1 of 1 The table to the right shows the digits of the hexadecimal system (base sixteen their equivalents in the binary system (base two). Use the table to fill in the blanks below. (a) Write 10111001011 (two) in the hexadecimal system. 10111001011 (two) = (sixteen) (b) Write 9D (sixteen) in the binary system. 9D (sixteen) = (two)

Solution Steps

To solve the given problems, we need to convert numbers between binary (base 2) and hexadecimal (base 16) systems.

(a) To convert a binary number to hexadecimal:

1. Group the binary digits into sets of four, starting from the right. Add leading zeros if necessary.
2. Convert each group of four binary digits to its hexadecimal equivalent.

(b) To convert a hexadecimal number to binary:

1. Convert each hexadecimal digit to its 4-bit binary equivalent.

To convert the binary number \( 10111001011 \) to hexadecimal, we first pad it with leading zeros to make its length a multiple of 4: \[ \text{Padded binary: } 010111001011 \] Next, we group the binary digits into sets of four: \[ \text{Groups: } 0101, 1100, 1011 \] Now, we convert each group to its hexadecimal equivalent: \[ 0101 \rightarrow 5, \quad 1100 \rightarrow C, \quad 1011 \rightarrow B \] Thus, we have: \[ 10111001011_{\text{two}} = 5CB_{\text{sixteen}} \]

To convert the hexadecimal number \( 9D \) to binary, we convert each hexadecimal digit to its 4-bit binary equivalent: \[ 9 \rightarrow 1001, \quad D \rightarrow 1101 \] Combining these gives: \[ 9D_{\text{sixteen}} = 10011101_{\text{two}} \]

Final Answer