Question

The hexadecimal equivalent of a digital number \(10011101\) is:

• A. H913
• B. 9D
• C. AE
• D. 157

Hint:

Group the eight bits into two nibbles of four and convert each nibble to a single hex digit.

Answer 1

The Correct Option is B

Step 1: A binary number is converted to hexadecimal by grouping the bits into sets of four, starting from the right (the least significant bit). Each group of four bits maps to exactly one hexadecimal digit, because \(2^4 = 16\).

Step 2: Split the eight-bit number \(10011101\) into two nibbles: \[1001 \quad\text{and}\quad 1101.\]
Step 3: Convert the left nibble \(1001\): \[1\cdot 8 + 0\cdot 4 + 0\cdot 2 + 1\cdot 1 = 9.\] In hexadecimal this is the digit \(9\).

Step 4: Convert the right nibble \(1101\): \[1\cdot 8 + 1\cdot 4 + 0\cdot 2 + 1\cdot 1 = 13.\] In hexadecimal the value \(13\) is written as the digit \(D\).

Step 5: Place the two hex digits side by side in the same order as the nibbles: \[10011101_2 = 9\mathrm{D}_{16}.\] So the correct choice is (B).

\[\boxed{9\mathrm{D}}\]