Decimal to Binary Conversion Quiz

The decimal number 5 is represented in binary as 101. This is derived from the binary place values: 1 (2^2) + 0 (2^1) + 1 (2^0) equals 4 + 0 + 1, which totals 5. Each digit in binary corresponds to a power of 2, making 101 the correct representation.

To convert the decimal number 12 to binary, we divide the number by 2 and record the remainders. Starting with 12, we divide: 12 ÷ 2 = 6 (remainder 0), 6 ÷ 2 = 3 (remainder 0), 3 ÷ 2 = 1 (remainder 1), and 1 ÷ 2 = 0 (remainder 1). Reading the remainders from bottom to top gives us 1100.

The binary number 1010 is calculated in decimal by taking each bit from right to left, starting with 2^0. This gives: 0×2^0 + 1×2^1 + 0×2^2 + 1×2^3, which equals 0 + 2 + 0 + 8, resulting in 10. Thus, the binary 1010 represents the decimal number 10.

To convert the decimal number 8 to binary, we divide the number by 2 and record the remainders. Starting from 8, we divide: 8 ÷ 2 = 4 (remainder 0), 4 ÷ 2 = 2 (remainder 0), 2 ÷ 2 = 1 (remainder 0), and finally 1 ÷ 2 = 0 (remainder 1). Reading the remainders in reverse gives us 1000.

To convert the decimal number 15 to binary, we divide by 2 and record the remainders. Starting from 15, the divisions yield remainders of 1 (for 15), 1 (for 7), 1 (for 3), and 1 (for 1). Reading the remainders from bottom to top gives us 1111, which represents 15 in binary.

To convert the decimal number 20 into binary, we divide it by 2 and record the remainders. Starting with 20, we get remainders of 0, 0, 1, 0, and 1, which, when read in reverse order, gives us 10100. This binary representation accurately reflects the value of 20 in decimal.

Binary 11 represents the number in base 2. Each digit corresponds to a power of 2: the rightmost digit is 2^0 (1) and the next is 2^1 (2). Therefore, adding these values together, 1 (from the rightmost digit) + 2 (from the next digit) equals 3 in decimal.

To convert the decimal number 7 to binary, we divide it by 2 and record the remainders. Dividing 7 by 2 gives a quotient of 3 and a remainder of 1. Dividing 3 by 2 gives a quotient of 1 and a remainder of 1. Finally, dividing 1 by 2 gives a quotient of 0 and a remainder of 1. Reading the remainders from bottom to top, we get 111.

The binary number 10000 represents a value in base 2, where each digit corresponds to a power of 2. Starting from the right, the digits are 0, 0, 0, 0, and 1, which translates to 1 × 2^4 = 16 in decimal. Thus, 10000 in binary equals 16 in decimal.

To convert the decimal number 25 to binary, divide the number by 2 repeatedly, noting the remainders. Starting with 25, the divisions yield remainders of 1, 0, 0, 1, and then 1, which read in reverse order gives 11001. Thus, the binary representation of decimal 25 is 11001.

To convert the decimal number 18 to binary, divide the number by 2 and record the remainder. Continuing this process, 18 divided by 2 gives a quotient of 9 and a remainder of 0. Repeating this until reaching 0, the remainders read in reverse order yield the binary representation: 10010.

To convert the binary number 1001 to decimal, we evaluate it based on powers of 2. Starting from the right, the digits represent \(2^0\), \(2^1\), \(2^2\), and \(2^3\). Thus, \(1 \times 2^3 + 0 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 8 + 0 + 0 + 1 = 9\).