Convert the following decimal numbers to binary: 1. 490₁₀ 2. 340₁₀
Answer (1)
To convert decimal numbers to binary, you repeatedly divide the number by 2 and record the remainder. You then read the remainders in reverse order to get the binary equivalent. Let's do this step-by-step for each number provided:
Convert 490 (in decimal) to binary :
Divide 490 by 2. Quotient is 245, remainder is 0.
Divide 245 by 2. Quotient is 122, remainder is 1.
Divide 122 by 2. Quotient is 61, remainder is 0.
Divide 61 by 2. Quotient is 30, remainder is 1.
Divide 30 by 2. Quotient is 15, remainder is 0.
Divide 15 by 2. Quotient is 7, remainder is 1.
Divide 7 by 2. Quotient is 3, remainder is 1.
Divide 3 by 2. Quotient is 1, remainder is 1.
Divide 1 by 2. Quotient is 0, remainder is 1.
Reading the remainders in reverse order, we get:
49 0 10 = 11110101 0 2
Convert 340 (in decimal) to binary :
Divide 340 by 2. Quotient is 170, remainder is 0.
Divide 170 by 2. Quotient is 85, remainder is 0.
Divide 85 by 2. Quotient is 42, remainder is 1.
Divide 42 by 2. Quotient is 21, remainder is 0.
Divide 21 by 2. Quotient is 10, remainder is 1.
Divide 10 by 2. Quotient is 5, remainder is 0.
Divide 5 by 2. Quotient is 2, remainder is 1.
Divide 2 by 2. Quotient is 1, remainder is 0.
Divide 1 by 2. Quotient is 0, remainder is 1.
Reading the remainders in reverse order, we get:
34 0 10 = 10101010 0 2
This method of conversion is widely used in computing because binary is the foundational language of computers, and understanding these conversions is essential for various applications in technology.
