Binary is a numerical system that utilizes only two digits: 0 and 1. It is also referred to as the base-2 system, in contrast to the base-10 system that is commonly used in everyday life. In binary, each digit corresponds to a power of 2, starting with 20 which equals 1 and doubling for each subsequent digit.
To convert a decimal number to binary, one can use the process of division by 2. This involves dividing the decimal number by 2 and keeping track of the remainder at each step. The remainders are read in reverse order to obtain the binary equivalent of the decimal number.
Here is the step-by-step process to convert the decimal number 12 into binary:
Step 1: Divide 12 by 2, resulting in a quotient of 6 and a remainder of 0. 12 ÷ 2 = 6 remainder 0
Step 2: Divide the quotient, which is 6, by 2 again, resulting in a quotient of 3 and a remainder of 0. 6 ÷ 2 = 3 remainder 0
Step 3: Divide the new quotient, which is 3, by 2 again, resulting in a quotient of 1 and a remainder of 1. 3 ÷ 2 = 1 remainder 1
Step 4: Divide the new quotient, which is 1, by 2 again, resulting in a quotient of 0 and a remainder of 1. 1 ÷ 2 = 0 remainder 1
Step 5: Read the remainders in reverse order, starting from the bottom, to obtain the binary equivalent of 12. 12 decimal = 1100 binary
Therefore, the binary equivalent of the decimal number 12 is 1100.
In binary, each digit corresponds to a power of 2, starting from 20 on the right and doubling for each subsequent digit to the left. The binary number 1100 can be expressed as:
123 + 122 + 021 + 020 = 8 + 4 + 0 + 0 = 12
Hence, the decimal equivalent of the binary number 1100 is 12.
In summary, converting a decimal number to binary involves dividing the decimal number by 2 and keeping track of the remainders at each step until the quotient becomes zero. The remainders are then read in reverse order to obtain the binary equivalent of the decimal number. In the case of the decimal number 12, the binary equivalent is 1100, which represents the value of 12 in the binary number system.