Question

Match the binary operations in List-I with correct results in List-II.

• A. a - ii, b - i, c - iv, d - iii
• B. a - iii, b - ii, c - iv, d - i
• C. a - ii, b - iii, c - i, d - iv
• D. a - i, b - v, c - ii, d - iii

Hint:

Memorize these important binary arithmetic facts: \[ 1+1=10 \] \[ 1\times0=0 \] \[ N\div1=N \] These simple rules help solve many binary arithmetic questions instantly.

Answer 1

The Correct Option is A

Concept: Binary arithmetic follows the same mathematical principles as decimal arithmetic but uses only two digits: \[ 0 \quad \text{and} \quad 1 \] Let us evaluate each operation individually.

Step 1: Evaluate (a) \(1+1\). In binary: \[ 1+1=10_2 \] Thus, \[ a \rightarrow ii \]

Step 2: Evaluate (b) \(10-1\). Convert to decimal: \[ 10_2=2_{10} \] \[ 2-1=1 \] Therefore, \[ 10_2-1_2=1_2 \] Thus, \[ b \rightarrow i \]

Step 3: Evaluate (c) \(1\times0\). Any number multiplied by zero gives zero. \[ 1\times0=0 \] Thus, \[ c \rightarrow iv \]

Step 4: Evaluate (d) \(11\div1\). Any number divided by one remains unchanged. \[ 11\div1=11 \] Thus, \[ d \rightarrow iii \]

Step 5: Writing the final matching. \[ a \rightarrow ii \] \[ b \rightarrow i \] \[ c \rightarrow iv \] \[ d \rightarrow iii \] Hence, the correct option is: \[ \boxed{(A)} \]