Base System – 7 Practice Questions Sum & Multiplication
July 8, 2024 2025-07-08 13:22Base System – 7 Practice Questions Sum & Multiplication
Base System – 7 Practice Questions Sum & Multiplication
Amiya Kumar 📘 Binary System Arithmetic – Questions 1 to 7 - By AMIYA
Solve these binary arithmetic questions. Click the button below each question to view the solution.
1. \( 1000_2 + 1101_2 + 1111_2 = \)
- 1. 100100
- 2. 111100
- 3. 101010
- 4. None of these
\[ 1000_2 = 8,\quad 1101_2 = 13,\quad 1111_2 = 15 \\ \text{Sum} = 8 + 13 + 15 = 36 \Rightarrow 36_{10} = 100100_2 \]
Answer: \( \boxed{1} \)
2. \( 111_2 + 101_2 + 011_2 = \)
- 1. 1011
- 2. 1111
- 3. 1101
- 4. None of these
\[ 111 = 7,\quad 101 = 5,\quad 011 = 3 \\ 7 + 5 + 3 = 15 \Rightarrow 1111_2 \]
Answer: \( \boxed{2} \)
3. \( 10001_2 - 1111_2 = \)
- 1. 101
- 2. 11
- 3. 10
- 4. None of these
\[ 10001_2 = 17,\quad 1111_2 = 15 \\ 17 - 15 = 2 \Rightarrow 10_2 \]
Answer: \( \boxed{3} \)
4. \( 11111_2 - 10001_2 = \)
- 1. 1010
- 2. 1111
- 3. 1110
- 4. None of these
\[ 11111 = 31,\quad 10001 = 17 \\ 31 - 17 = 14 \Rightarrow 1110_2 \]
Answer: \( \boxed{3} \)
5. Multiply \( 101_2 \times 11_2 \)
- 1. 1111
- 2. 1011
- 3. 1110
- 4. 11011
- 5. None of these
\[ 101 = 5,\quad 11 = 3,\quad 5 \times 3 = 15 \Rightarrow 1111_2 \]
Answer: \( \boxed{1} \)
6. Multiply \( 11001_2 \times 101_2 \)
- 1. 1111101
- 2. 1110101
- 3. 1011101
- 4. 1100110
- 5. None of these
\[ 11001 = 25,\quad 101 = 5 \\ 25 \times 5 = 125 \Rightarrow 1111101_2 \]
Answer: \( \boxed{1} \)
7. How many of the following binary numbers are divisible by \( 2_{10} \)?
(i) 110101, (ii) 110010, (iii) 11111, (iv) 100010
- 1. 0
- 2. 1
- 3. 2
- 4. 3
- 5. 4
Binary numbers ending with 0 are divisible by 2.
(ii) 110010 and (iv) 100010 end with 0 → divisible
Answer: \( \boxed{2} \)
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