NIMCET 2014 — Reasoning PYQ

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 $1$.

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

Step 2: Conversion to Decimal

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

Calculate the values:

• $1\times 4096=4096$

• $5\times 256=1280$

• $3\times 16=48$

• $1\times 1=1$

Summing them up:

Conclusion:

The decimal equivalent of the operation is 5425.