Year 8 - L5 Homework

Q1: What is the correct binary conversion of denary: 41

• 00101001

• 00101011

• 00101000

• 00001001

Answer explanation

The correct binary conversion of denary 41 is 00101001 because 41 is represented as 32 + 8 + 1 in binary which translates to 00101001.

Q2. What is the correct binary conversion of denary: 36

• 00100110

• 00100100

• 00100101

• 00100111

Answer explanation

The correct binary conversion of denary 36 is 00100100, which is the second option provided.

Q3. What is the correct binary conversion of denary: 129

• 10000001

• 10000011

• 11000001

• 10010001

Answer explanation

The correct binary conversion of denary 129 is 10000001, as each digit represents a power of 2 starting from the right.

Q4. What is the correct binary conversion of denary: 106

• 1101011

• 1101010

• 1101111

• 1111010

Answer explanation

The correct binary conversion of denary 106 is 1101010. To convert, divide 106 by 2 repeatedly and note the remainders from bottom to top.

Q5. What is the correct binary conversion of denary: 51

• 111111

• 110111

• 110011

Answer explanation

The correct binary conversion of denary 51 is 110011. To convert decimal to binary, divide the number by 2 and note the remainders from bottom to top.

Q6. What is the correct binary conversion of denary: 47

• 100011

• 111111

• 101111

• 101011

Answer explanation

The correct binary conversion of denary 47 is 101111 because 47 divided by 2 gives a remainder of 1, and the process is repeated until the quotient is 0, reading the remainders from bottom to top.

Q7. What is the correct binary conversion of denary: 23

• 10100

• 00111

• 11111

• 10111

Answer explanation

The correct binary conversion of denary 23 is 10111, which matches the fourth answer choice.

Q8. What is the correct denary conversion of binary: 101010

• 42

• 43

• 45

• 150

Answer explanation

To convert binary 101010 to denary, we use the formula: (1*2^5) + (0*2^4) + (1*2^3) + (0*2^2) + (1*2^1) + (0*2^0) = 32 + 0 + 8 + 0 + 2 + 0 = 42. Therefore, the correct denary conversion is 42.

Q9. What is the correct denary conversion of binary: 111111

• 66

• 63

• 57

• 21

Answer explanation

To convert binary 111111 to denary, we add the decimal values of each bit: 1*2^5 + 1*2^4 + 1*2^3 + 1*2^2 + 1*2^1 + 1*2^0 = 63. Therefore, the correct denary conversion is 63.

Q10. What is the correct denary conversion of binary: 10000001

• 36

• 13

• 129

• 189

Answer explanation

To convert binary 10000001 to denary, we add the decimal values of the positions with 1s: 2^7 + 2^0 = 128 + 1 = 129. Therefore, the correct denary conversion is 129.