Number Base worksheet - Free Printable

To solve the binary multiplication problems, we will follow the standard rules of binary arithmetic. Binary multiplication is similar to decimal multiplication but uses only two digits: 0 and 1. Here are the steps for each problem:

Problem 1: \( 1101 \times 11 \)

1. Multiply \( 1101 \) by the rightmost digit of \( 11 \) (which is 1):
\[
1101 \times 1 = 1101
\]
2. Multiply \( 1101 \) by the next digit of \( 11 \) (which is 1), and shift left by one position:
\[
1101 \times 1 = 1101 \quad \text{(shift left)} \quad \Rightarrow \quad 11010
\]
3. Add the results:
\[
1101 + 11010 = 100111
\]

Answer: \( 100111 \)

Problem 2: \( 11101 \times 111 \)

1. Multiply \( 11101 \) by the rightmost digit of \( 111 \) (which is 1):
\[
11101 \times 1 = 11101
\]
2. Multiply \( 11101 \) by the next digit of \( 111 \) (which is 1), and shift left by one position:
\[
11101 \times 1 = 11101 \quad \text{(shift left)} \quad \Rightarrow \quad 111010
\]
3. Multiply \( 11101 \) by the next digit of \( 111 \) (which is 1), and shift left by two positions:
\[
11101 \times 1 = 11101 \quad \text{(shift left twice)} \quad \Rightarrow \quad 1110100
\]
4. Add the results:
\[
11101 + 111010 + 1110100 = 10101111
\]

Answer: \( 10101111 \)

Problem 3: \( 11101 \times 111 \)

This is the same as Problem 2, so the answer is:

Answer: \( 10101111 \)

Problem 4: \( 1101101 \times 101 \)

1. Multiply \( 1101101 \) by the rightmost digit of \( 101 \) (which is 1):
\[
1101101 \times 1 = 1101101
\]
2. Multiply \( 1101101 \) by the next digit of \( 101 \) (which is 0), and shift left by one position:
\[
1101101 \times 0 = 0 \quad \text{(shift left)} \quad \Rightarrow \quad 0
\]
3. Multiply \( 1101101 \) by the next digit of \( 101 \) (which is 1), and shift left by two positions:
\[
1101101 \times 1 = 1101101 \quad \text{(shift left twice)} \quad \Rightarrow \quad 110110100
\]
4. Add the results:
\[
1101101 + 0 + 110110100 = 111100001
\]

Answer: \( 111100001 \)

Problem 5: \( 101101 \times 11 \)

1. Multiply \( 101101 \) by the rightmost digit of \( 11 \) (which is 1):
\[
101101 \times 1 = 101101
\]
2. Multiply \( 101101 \) by the next digit of \( 11 \) (which is 1), and shift left by one position:
\[
101101 \times 1 = 101101 \quad \text{(shift left)} \quad \Rightarrow \quad 1011010
\]
3. Add the results:
\[
101101 + 1011010 = 1111111
\]

Answer: \( 1111111 \)

Problem 6: \( 1110011 \times 101 \)

1. Multiply \( 1110011 \) by the rightmost digit of \( 101 \) (which is 1):
\[
1110011 \times 1 = 1110011
\]
2. Multiply \( 1110011 \) by the next digit of \( 101 \) (which is 0), and shift left by one position:
\[
1110011 \times 0 = 0 \quad \text{(shift left)} \quad \Rightarrow \quad 0
\]
3. Multiply \( 1110011 \) by the next digit of \( 101 \) (which is 1), and shift left by two positions:
\[
1110011 \times 1 = 1110011 \quad \text{(shift left twice)} \quad \Rightarrow \quad 111001100
\]
4. Add the results:
\[
1110011 + 0 + 111001100 = 1001110011
\]

Answer: \( 1001110011 \)

Problem 7: \( 1111 \times 10 \)

1. Multiply \( 1111 \) by the rightmost digit of \( 10 \) (which is 0):
\[
1111 \times 0 = 0
\]
2. Multiply \( 1111 \) by the next digit of \( 10 \) (which is 1), and shift left by one position:
\[
1111 \times 1 = 1111 \quad \text{(shift left)} \quad \Rightarrow \quad 11110
\]
3. Add the results:
\[
0 + 11110 = 11110
\]

Answer: \( 11110 \)

Problem 8: \( 101110 \times 111 \)

1. Multiply \( 101110 \) by the rightmost digit of \( 111 \) (which is 1):
\[
101110 \times 1 = 101110
\]
2. Multiply \( 101110 \) by the next digit of \( 111 \) (which is 1), and shift left by one position:
\[
101110 \times 1 = 101110 \quad \text{(shift left)} \quad \Rightarrow \quad 1011100
\]
3. Multiply \( 101110 \) by the next digit of \( 111 \) (which is 1), and shift left by two positions:
\[
101110 \times 1 = 101110 \quad \text{(shift left twice)} \quad \Rightarrow \quad 10111000
\]
4. Add the results:
\[
101110 + 1011100 + 10111000 = 100010010
\]

Answer: \( 100010010 \)

Problem 9: \( 110011 \times 11 \)

1. Multiply \( 110011 \) by the rightmost digit of \( 11 \) (which is 1):
\[
110011 \times 1 = 110011
\]
2. Multiply \( 110011 \) by the next digit of \( 11 \) (which is 1), and shift left by one position:
\[
110011 \times 1 = 110011 \quad \text{(shift left)} \quad \Rightarrow \quad 1100110
\]
3. Add the results:
\[
110011 + 1100110 = 10011001
\]

Answer: \( 10011001 \)

Problem 10: \( 1101 \times 101 \)

1. Multiply \( 1101 \) by the rightmost digit of \( 101 \) (which is 1):
\[
1101 \times 1 = 1101
\]
2. Multiply \( 1101 \) by the next digit of \( 101 \) (which is 0), and shift left by one position:
\[
1101 \times 0 = 0 \quad \text{(shift left)} \quad \Rightarrow \quad 0
\]
3. Multiply \( 1101 \) by the next digit of \( 101 \) (which is 1), and shift left by two positions:
\[
1101 \times 1 = 1101 \quad \text{(shift left twice)} \quad \Rightarrow \quad 110100
\]
4. Add the results:
\[
1101 + 0 + 110100 = 111001
\]

Answer: \( 111001 \)

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & 100111 \\
2. & 10101111 \\
3. & 10101111 \\
4. & 111100001 \\
5. & 1111111 \\
6. & 1001110011 \\
7. & 11110 \\
8. & 100010010 \\
9. & 10011001 \\
10. & 111001 \\
\end{array}
}
\]