Mathematics Form 4 Chapter 2 - Number Bases

Convert the number 1011 from base 2 to base 10.

• 101

• 11

• 1001

• 1100

Answer explanation

To convert from base 2 to base 10, multiply each digit by 2 raised to the power of its position from right to left. In this case, 1*2^3 + 0*2^2 + 1*2^1 + 1*2^0 = 8 + 0 + 2 + 1 = 11. Therefore, the correct answer is 11.

What is the result of adding 23 base 8 and 15 base 8?

• 31

• 40

• 37

• 56

Answer explanation

To add 23 base 8 and 15 base 8, we perform the addition as we would in base 10, which gives us 40 in base 8. Therefore, the result is 40.

Convert 138 base 10 to base 5.

• 1023

• 1032

• 1133

• 1223

Answer explanation

To convert 138 base 10 to base 5, divide 138 by 5 which gives 27 with a remainder of 3. Then divide 27 by 5 which gives 5 with a remainder of 2. Finally, divide 5 by 5 which gives 1 with a remainder of 0. Reading remainders from bottom to top gives 1023 in base 5.

Convert the 75 base 10 to base 2.

• 1001011

• 1110000

• 1100101

• 1011010

Answer explanation

To convert 75 base 10 to base 2, divide by 2 repeatedly and take remainders. The remainders in reverse order give 1001011.

Subtract 1101 base 2 from 10000 base 2.

• 1001

• 111

• 101

• 11

Answer explanation

To subtract 1101 from 10000 in base 2, perform binary subtraction. Borrowing is needed, resulting in 11 as the correct answer.

Convert the number 123 base 4 to base 10.

• 19

• 27

• 35

• 42

Answer explanation

To convert 123 base 4 to base 10, we use the formula: (1 * 4^2) + (2 * 4^1) + (3 * 4^0) = 27. Therefore, the correct answer is 27.

What is the base of the number 17?

• 20

• 8

• 16

• 10

Answer explanation

The base of the number 17 is 10 because the number 17 is in base 10, which is the standard decimal system we commonly use.

Convert 98 base 10 to base 5.

• 235

• 452

• 567

• 343

Answer explanation

To convert 98 base 10 to base 5, divide 98 by 5 which gives 19 with a remainder of 3. Then divide 19 by 5 which gives 3 with a remainder of 4. The remainders in reverse order are 34, so the answer is 343 in base 5.

Add 23 base 6 and 14 base 6.

• 48

• 35

• 37

• 41

Answer explanation

To add 23 base 6 and 14 base 6, we get 41 in base 6. Therefore, the correct answer is 41.

Convert the number 101010 base 2 to base 10.

• 42

• 38

• 24

• 56

Answer explanation

To convert 101010 base 2 to base 10, 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 answer is 42.