HT2 Y8 EAGER Test Prep

Which of the following is the correct binary addition for `110` + `11`?

• `1001`

• `111`

• `100`

• `1101`

Answer explanation

To add `110` (6 in decimal) and `11` (3 in decimal) in binary, align them: 110 + 11 ------ 1101 This results in `1101`, which is 9 in decimal, confirming that `1101` is the correct answer.

What is the binary equivalent of adding `13` and `7` in decimal?

• `10000`

• `10100`

• `11010`

• `11100`

Answer explanation

To find the binary equivalent of adding 13 and 7, first calculate 13 + 7 = 20 in decimal. The binary representation of 20 is `11100`, which is the correct answer.

Convert the decimal number `13` to binary.

• `1010`

• `1100`

• `1110`

• `1101`

Answer explanation

To convert the decimal number 13 to binary, divide by 2 and record the remainders. 13 ÷ 2 = 6 remainder 1, 6 ÷ 2 = 3 remainder 0, 3 ÷ 2 = 1 remainder 1, 1 ÷ 2 = 0 remainder 1. Reading the remainders from bottom to top gives 1101.

Convert the binary number `10110` to decimal.

• 21

• 22

• 23

• 20

Answer explanation

To convert the binary number `10110` to decimal, calculate: 1*2^4 + 0*2^3 + 1*2^2 + 1*2^1 + 0*2^0 = 16 + 0 + 4 + 2 + 0 = 22. Thus, the correct answer is 22.

True or False: Binary numbers can only be made up of the digits 0 and 1.

• True

• False

Answer explanation

True. Binary numbers are a base-2 numeral system that exclusively uses the digits 0 and 1. Therefore, the statement is correct.

Convert the decimal number `42` to binary.

• `101010`

• `110010`

• `101110`

• `111010`

Answer explanation

To convert the decimal number 42 to binary, divide by 2 and record the remainders. 42 ÷ 2 = 21 (0), 21 ÷ 2 = 10 (1), 10 ÷ 2 = 5 (0), 5 ÷ 2 = 2 (1), 2 ÷ 2 = 1 (0), 1 ÷ 2 = 0 (1). Reading the remainders from bottom to top gives `101010`.

Convert the binary number `111` to decimal.

• 5

• 6

• 7

• 8

Answer explanation

To convert the binary number `111` to decimal, calculate: 1*(2^2) + 1*(2^1) + 1*(2^0) = 4 + 2 + 1 = 7. Thus, the correct answer is 7.

What is the smallest decimal number that can be represented in binary?

• 0

• 1

• 2

• -1

Answer explanation

The smallest decimal number that can be represented in binary is 0. Binary representation uses bits, and 0 is the lowest value, while 1 and 2 are greater, and -1 is not a valid binary representation.

True or False: The binary number `1000` is equal to 8 in decimal.

• True

• False

Answer explanation

The binary number `1000` represents 1 in the 2^3 place, which equals 8 in decimal. Therefore, the statement is True.

True or False: The NOT operator inverts the input value.

• True

• False

Answer explanation

True. The NOT operator is a logical operator that inverts the input value, meaning it changes true to false and false to true.