NIMCET 2024 — Computer PYQ

Decimal Conversion Verification

To double-check our work, we can easily convert both values to base-10 decimal numbers, perform the operation, and convert back.

1. Convert the Dividend to Decimal:

$$11010111_2=(1\times 2^7)+(1\times 2^6)+(0\times 2^5)+(1\times 2^4)+(0\times 2^3)+(1\times 2^2)+(1\times 2^1)+(1\times 2^0)$$

$$=128+64+0+16+0+4+2+1=215_{10}$$

2. Convert the Divisor to Decimal:

$$101_2=(1\times 2^2)+(0\times 2^1)+(1\times 2^0)=4+0+1=5_{10}$$

3. Perform the Division in Decimal:

$$\text{Quotient}=\frac{215}{5}=43_{10}$$

4. Convert the Decimal Quotient Back to Binary:

Let's find the binary representation for the decimal value $43$:

• $43-32=11\to 2^5=1$

• $11-8=3\to 2^3=1$

• $3-2=1\to 2^1=1$

• $1-1=0\to 2^0=1$

$$43_{10}=32+8+2+1=2^5+2^3+2^1+2^0$$

Writing out the complete positional bit string gives us:

$$43_{10}=101011_2$$

Both calculation methods align perfectly, verifying that Option D is correct.