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

Method: full decimal cross-check.

First find the plain decimal value of the binary string $10011101$ by adding the place values of every bit that is a $1$. The bit positions from the right carry weights $1, 2, 4, 8, 16, 32, 64, 128$: $$128 + 0 + 0 + 16 + 8 + 4 + 0 + 1 = 157.$$

Now convert $157$ to base $16$ by repeated division. Divide by $16$: $157 = 9\times 16 + 13$, so the least significant hex digit is the remainder $13$, which is the symbol $D$, and the quotient is $9$. Divide the quotient $9$ by $16$: $9 = 0\times 16 + 9$, giving the next digit $9$ and quotient $0$, so we stop.

Reading the remainders from last to first gives the hex digits $9$ then $D$, i.e. $$157_{10} = 9D_{16}.$$

Both routes agree: the eight bits pack into two hex digits $9$ and $D$. Note that option (D) $157$ is just the decimal value written out, not the hexadecimal, so it is a distractor.

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