NIMCET 2014 — Reasoning PYQ

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Question

NIMCET 2014 — Reasoning PYQ

NIMCET | Reasoning | 2014

The decimal equivalent of the hexadecimal operation A10 + B21 is

Choose the correct answer:

Explanation

Solution

To solve this, we first perform the hexadecimal addition and then convert the result into a decimal number.

Step 1: Hexadecimal Addition

We add the numbers column by column. Remember that in Hexadecimal:

$A = 10$ and $B = 11$ .

Column 1 (Right): $0 + 1 = 1$
Column 2 (Middle): $1 + 2 = 3$
Column 3 (Left): $A + B = 10 + 11 = 21$
- Since $21$ is greater than the base ( $16$ ), we calculate: $21 - 16 = 5$ with a carry of $1$ .

\begin{array}{r@{\quad}c@{\quad}c@{\quad}c} & A & 1 & 0 \\ + & B & 2 & 1 \\ \hline 1 & 5 & 3 & 1 \end{array}

So, $(A10)_{16} + (B21)_{16} = (1531)_{16}$ .

Step 2: Conversion to Decimal

Now, convert $(1531)_{16}$ to its decimal equivalent using powers of $16$ :

(1531)_{16} = (1 \times 16^{3}) + (5 \times 16^{2}) + (3 \times 16^{1}) + (1 \times 16^{0})

Calculate the values:

$1 \times 4096 = 4096$
$5 \times 256 = 1280$
$3 \times 16 = 48$
$1 \times 1 = 1$

Summing them up:

4096 + 1280 + 48 + 1 = 5425

Conclusion:

The decimal equivalent of the operation is 5425.