1. **Stating the problem:** We need to find the bitwise OR, AND, and XOR for each pair of bit strings. 2. Let's evaluate each pair: **a) 1011110 and 0100001** (aligning bits as 7 bits): - Bitwise OR: $1011110 \,\text{OR}\, 0100001 = 1111111$ - Bitwise AND: $1011110 \,\text{AND}\, 0100001 = 0000000$ - Bitwise XOR: $1011110 \,\text{XOR}\, 0100001 = 1111111$ **b) 11110000 and 10101010 (8 bits):** - Bitwise OR: $11110000 \,\text{OR}\, 10101010 = 11111010$ - Bitwise AND: $11110000 \,\text{AND}\, 10101010 = 10100000$ - Bitwise XOR: $11110000 \,\text{XOR}\, 10101010 = 01011010$ **c) 0001110001 and 1001001000 (10 bits):** - Bitwise OR: $0001110001 \,\text{OR}\, 1001001000 = 1001111001$ - Bitwise AND: $0001110001 \,\text{AND}\, 1001001000 = 0001000000$ - Bitwise XOR: $0001110001 \,\text{XOR}\, 1001001000 = 1000111001$ **d) 1111111111 and 0000000000 (10 bits):** - Bitwise OR: $1111111111 \,\text{OR}\, 0000000000 = 1111111111$ - Bitwise AND: $1111111111 \,\text{AND}\, 0000000000 = 0000000000$ - Bitwise XOR: $1111111111 \,\text{XOR}\, 0000000000 = 1111111111$ 3. **Final answers:** a) OR = 1111111, AND = 0000000, XOR = 1111111 b) OR = 11111010, AND = 10100000, XOR = 01011010 c) OR = 1001111001, AND = 0001000000, XOR = 1000111001 d) OR = 1111111111, AND = 0000000000, XOR = 1111111111