NIMCET 2013 — Computer PYQ

Solution

The correct option is 3.

Step 1: Convert binary numbers to decimal

• For $(10111{)}_2$:

  $$(1\times 2^4)+(0\times 2^3)+(1\times 2^2)+(1\times 2^1)+(1\times 2^0)=16+0+4+2+1=(23{)}_{10}$$

• For $(1110{)}_2$:

  $$(1\times 2^3)+(1\times 2^2)+(1\times 2^1)+(0\times 2^0)=8+4+2+0=(14{)}_{10}$$

Step 2: Perform the multiplication in decimal

Step 3: Convert the decimal result to Hexadecimal (Base 16)

To convert $(322{)}_{10}$ to hex, we divide by $16$ repeatedly:

• $322÷16=20$ with a remainder of $2$ (Hex: $2$)

• $20÷16=1$ with a remainder of $4$ (Hex: $4$)

• $1÷16=0$ with a remainder of $1$ (Hex: $1$)

Reading the remainders from bottom to top, we get $(142{)}_{16}$.