Question

257 в десятиричной системе счисления= ?в двоичной системе счисления.

Answer 1

$100000001 {}^{2}$

Answer 2

To convert the number 257 from the decimal system to the binary system, we can use the process of repeated division by 2. Here's the step-by-step conversion:

Step 1: Divide 257 by 2, and note down the quotient and remainder. 257 ÷ 2 = 128 with a remainder of 1

Step 2: Divide the quotient (128) from Step 1 by 2, and note down the new quotient and remainder. 128 ÷ 2 = 64 with a remainder of 0

Step 3: Divide the quotient (64) from Step 2 by 2 again. 64 ÷ 2 = 32 with a remainder of 0

Step 4: Divide the quotient (32) from Step 3 by 2 again. 32 ÷ 2 = 16 with a remainder of 0

Step 5: Divide the quotient (16) from Step 4 by 2 again. 16 ÷ 2 = 8 with a remainder of 0

Step 6: Divide the quotient (8) from Step 5 by 2 again. 8 ÷ 2 = 4 with a remainder of 0

Step 7: Divide the quotient (4) from Step 6 by 2 again. 4 ÷ 2 = 2 with a remainder of 0

Step 8: Divide the quotient (2) from Step 7 by 2 again. 2 ÷ 2 = 1 with a remainder of 0

Step 9: Divide the quotient (1) from Step 8 by 2 again. 1 ÷ 2 = 0 with a remainder of 1

Now, read the remainders from bottom to top, and we get the binary representation of 257:

257 (decimal) = 100000001 (binary)

So, 257 in the decimal system is equal to 100000001 in the binary system.