Binary to Decimal Conversion Quiz for Grade 7

1. What is the decimal value of the binary number 1010?

8

10

12

14

To convert the binary number 1010 to decimal, each digit represents a power of 2, starting from the right. In this case, 1×2^3 (8) + 0×2^2 (0) + 1×2^1 (2) + 0×2^0 (0) equals 8 + 0 + 2 + 0, which totals 10. Thus, the decimal value is 10.

Explanation

To convert the binary number 1010 to decimal, each digit represents a power of 2, starting from the right. In this case, 1×2^3 (8) + 0×2^2 (0) + 1×2^1 (2) + 0×2^0 (0) equals 8 + 0 + 2 + 0, which totals 10. Thus, the decimal value is 10.

2. Convert the binary number 1101 to decimal.

11

12

13

15

To convert the binary number 1101 to decimal, each digit represents a power of 2, starting from the right. The calculation is: \(1 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0\), which equals \(8 + 4 + 0 + 1 = 13\). Thus, 1101 in binary is 13 in decimal.

Explanation

To convert the binary number 1101 to decimal, each digit represents a power of 2, starting from the right. The calculation is: \(1 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0\), which equals \(8 + 4 + 0 + 1 = 13\). Thus, 1101 in binary is 13 in decimal.

3. In binary, the rightmost digit represents 2 to the power of ____.

In binary representation, each digit corresponds to a power of 2, starting from the rightmost digit. The rightmost digit, or least significant bit, represents \(2^0\), which equals 1. This foundational principle of binary numbering illustrates how values are assigned based on their position, with the rightmost position always representing the smallest power of 2.

Explanation

In binary representation, each digit corresponds to a power of 2, starting from the rightmost digit. The rightmost digit, or least significant bit, represents \(2^0\), which equals 1. This foundational principle of binary numbering illustrates how values are assigned based on their position, with the rightmost position always representing the smallest power of 2.

Submit

4. What is 10011 in decimal?

17

18

19

20

To convert the binary number 10011 to decimal, you multiply each digit by 2 raised to the power of its position, counting from right to left, starting at 0. This gives: \(1 \times 2^4 + 0 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 16 + 0 + 0 + 2 + 1 = 19\).

Explanation

To convert the binary number 10011 to decimal, you multiply each digit by 2 raised to the power of its position, counting from right to left, starting at 0. This gives: \(1 \times 2^4 + 0 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 16 + 0 + 0 + 2 + 1 = 19\).

5. The binary number 11111 equals ____ in decimal.

To convert the binary number 11111 to decimal, multiply each bit by 2 raised to the power of its position, starting from 0 on the right. This gives: \(1 \times 2^4 + 1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 16 + 8 + 4 + 2 + 1 = 31\).

Explanation

To convert the binary number 11111 to decimal, multiply each bit by 2 raised to the power of its position, starting from 0 on the right. This gives: \(1 \times 2^4 + 1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 16 + 8 + 4 + 2 + 1 = 31\).

Submit

6. Convert 100110 to decimal.

32

36

38

42

To convert the binary number 100110 to decimal, calculate its value by assigning powers of 2 to each digit from right to left. This gives: \(1 \times 2^5 + 0 \times 2^4 + 0 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 0 \times 2^0 = 32 + 0 + 0 + 4 + 2 + 0 = 36\).

Explanation

To convert the binary number 100110 to decimal, calculate its value by assigning powers of 2 to each digit from right to left. This gives: \(1 \times 2^5 + 0 \times 2^4 + 0 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 0 \times 2^0 = 32 + 0 + 0 + 4 + 2 + 0 = 36\).

7. What is the decimal equivalent of binary 1001?

8

9

10

11

To convert the binary number 1001 to decimal, each digit is multiplied by 2 raised to the power of its position from the right, starting at 0. Thus, 1*(2^3) + 0*(2^2) + 0*(2^1) + 1*(2^0) equals 8 + 0 + 0 + 1, which totals 9.

Explanation

To convert the binary number 1001 to decimal, each digit is multiplied by 2 raised to the power of its position from the right, starting at 0. Thus, 1*(2^3) + 0*(2^2) + 0*(2^1) + 1*(2^0) equals 8 + 0 + 0 + 1, which totals 9.

8. Binary 10000 equals ____ in decimal.

Binary 10000 represents the number in base 2. Each digit corresponds to a power of 2, starting from the right: 0 (2^0), 0 (2^1), 0 (2^2), 0 (2^3), and 1 (2^4). Thus, 1 × 2^4 equals 16, making the decimal equivalent of binary 10000 equal to 16.

Explanation

Binary 10000 represents the number in base 2. Each digit corresponds to a power of 2, starting from the right: 0 (2^0), 0 (2^1), 0 (2^2), 0 (2^3), and 1 (2^4). Thus, 1 × 2^4 equals 16, making the decimal equivalent of binary 10000 equal to 16.

Submit

9. Convert 11010 to decimal.

24

25

26

27

To convert the binary number 11010 to decimal, we calculate the value of each bit. Starting from the right, the bits represent 2^0, 2^1, 2^2, 2^3, and 2^4. Thus, 0×1 + 1×2 + 0×4 + 1×8 + 1×16 = 0 + 2 + 0 + 8 + 16 = 26.

Explanation

To convert the binary number 11010 to decimal, we calculate the value of each bit. Starting from the right, the bits represent 2^0, 2^1, 2^2, 2^3, and 2^4. Thus, 0×1 + 1×2 + 0×4 + 1×8 + 1×16 = 0 + 2 + 0 + 8 + 16 = 26.

10. What does binary 101101 equal in decimal?

43

44

45

46

To convert the binary number 101101 to decimal, you calculate the value of each bit from right to left, starting at 0. This gives you: \(1 \times 2^5 + 0 \times 2^4 + 1 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0\), which equals \(32 + 0 + 8 + 4 + 0 + 1 = 45\).

Explanation

To convert the binary number 101101 to decimal, you calculate the value of each bit from right to left, starting at 0. This gives you: \(1 \times 2^5 + 0 \times 2^4 + 1 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0\), which equals \(32 + 0 + 8 + 4 + 0 + 1 = 45\).

11. The binary number 1111 converts to ____ in decimal.

To convert the binary number 1111 to decimal, calculate it using powers of 2. Starting from the right, each digit represents a power of 2: \(1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0\), which equals \(8 + 4 + 2 + 1 = 15\). Thus, 1111 in binary is 15 in decimal.

Explanation

To convert the binary number 1111 to decimal, calculate it using powers of 2. Starting from the right, each digit represents a power of 2: \(1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0\), which equals \(8 + 4 + 2 + 1 = 15\). Thus, 1111 in binary is 15 in decimal.

Submit

12. Convert 110011 to decimal.

49

50

51

52

To convert the binary number 110011 to decimal, calculate the sum of the powers of 2 for each bit that is set to 1. Starting from the right, the calculation is: \(1 \times 2^0 + 1 \times 2^1 + 0 \times 2^2 + 0 \times 2^3 + 1 \times 2^4 + 1 \times 2^5\), which equals 51.

Explanation

To convert the binary number 110011 to decimal, calculate the sum of the powers of 2 for each bit that is set to 1. Starting from the right, the calculation is: \(1 \times 2^0 + 1 \times 2^1 + 0 \times 2^2 + 0 \times 2^3 + 1 \times 2^4 + 1 \times 2^5\), which equals 51.