Final answer:
To convert a decimal number to binary, divide by 2 repeatedly and read the remainders in reverse. To convert binary to decimal, use the place value method. (525)₁₀ = (1000001101)₂.
Step-by-step explanation:
To convert a decimal number to binary, we can use the method of repeated division by 2. Let's convert (525)10 to binary:
Step 1: Divide 525 by 2, which gives a quotient of 262 and a remainder of 1.
Step 2: Divide 262 by 2, which gives a quotient of 131 and a remainder of 0.
Step 3: Divide 131 by 2, which gives a quotient of 65 and a remainder of 1.
Step 4: Divide 65 by 2, which gives a quotient of 32 and a remainder of 1.
Step 5: Divide 32 by 2, which gives a quotient of 16 and a remainder of 0.
Step 6: Divide 16 by 2, which gives a quotient of 8 and a remainder of 0.
Step 7: Divide 8 by 2, which gives a quotient of 4 and a remainder of 0.
Step 8: Divide 4 by 2, which gives a quotient of 2 and a remainder of 0.
Step 9: Divide 2 by 2, which gives a quotient of 1 and a remainder of 0.
Step 10: Divide 1 by 2, which gives a quotient of 0 and a remainder of 1.
Reading the remainders from bottom to top, we get (1000001101)2 as the binary representation of (525)10.
To convert a binary number to decimal, we can use the place value method. Each digit in a binary number represents a power of 2. Let's convert (1000001101)2 to decimal:
(1000001101)2 = 1 × 2^9 + 0 × 2^8 + 0 × 2^7 + 0 × 2^6 + 0 × 2^5 + 0 × 2^4 + 1 × 2^3 + 1 × 2^2 + 0 × 2^1 + 1 × 2^0
= 512 + 0 + 0 + 0 + 0 + 0 + 8 + 4 + 0 + 1
= 525