NIMCET 2026 — Computer PYQ

Decimal Conversion Method (Verification)

1. Convert the first binary number to decimal:

   $$1100_2=(1\times 2^3)+(1\times 2^2)+(0\times 2^1)+(0\times 2^0)=8+4+0+0=12_{10}$$

2. Convert the second binary number to decimal:

   $$1011_2=(1\times 2^3)+(0\times 2^2)+(1\times 2^1)+(1\times 2^0)=8+0+2+1=11_{10}$$

3. Multiply the decimal numbers:

   $$12\times 11=132_{10}$$

4. Convert the product $132_{10}$ back to binary:

   • $132÷2=66$ with remainder 0 (Least Significant Bit)

   • $66÷2=33$ with remainder 0

   • $33÷2=16$ with remainder 1

   • $16÷2=8$ with remainder 0

   • $8÷2=4$ with remainder 0

   • $4÷2=2$ with remainder 0

   • $2÷2=1$ with remainder 0

   • $1÷2=0$ with remainder 1 (Most Significant Bit)

Reading the remainders from bottom to top gives:

$$10000100_2$$

.

Both methods yield the same result, confirming option 2 is correct.