Question

Convert the following Decimal Number into Binary numbers:
i) 257
ii) 96

Please send the sum and answers ​

Answer 1

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How to Convert 257 to Binary

Decimal to Binary

Here we will show you step-by-step how to convert the decimal number 257 to binary.

First, note that decimal numbers use 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) and binary numbers use only 2 digits (0 and 1).

As we explain the steps to converting 257 to binary, it is important to know the name of the parts of a division problem. In a problem like A divided by B equals C, A is the Dividend, B is the Divisor and C is the Quotient.

The Quotient has two parts. The Whole part and the Fractional part. The Fractional part is also known as the Remainder.

Step 1) Divide 257 by 2 to get the Quotient. Keep the Whole part for the next step and set the Remainder aside.

Step 2) Divide the Whole part of the Quotient from Step 1 by 2. Again, keep the Whole part and set the Remainder aside.

Step 3) Repeat Step 2 above until the Whole part is 0.

Step 4) Write down the Remainders in reverse order to get the answer to 257 as a binary.

Here we will show our work so you can follow along:

257 / 2 = 128 with 1 remainder

128 / 2 = 64 with 0 remainder

64 / 2 = 32 with 0 remainder

32 / 2 = 16 with 0 remainder

16 / 2 = 8 with 0 remainder

8 / 2 = 4 with 0 remainder

4 / 2 = 2 with 0 remainder

2 / 2 = 1 with 0 remainder

1 / 2 = 0 with 1 remainder

Then, when we put the remainders together in reverse order, we get the answer. The decimal number 257 converted to binary is therefore:

100000001

(ii) - step 1 Perform the successive MOD operation by 2 for the given decimal number 96 and note down the remainder (either 0 or 1) for each operation. The last remainder is the MSB (most significant bit) and the first remainder is the LSB (least significant bit).

96 / 2 = 48 : Remainder is 0 → LSB

48 / 2 = 24 : Remainder is 0

24 / 2 = 12 : Remainder is 0

12 / 2 = 6 : Remainder is 0

6 / 2 = 3 : Remainder is 0

3 / 2 = 1 : Remainder is 1

1 / 2 = 0 : Remainder is 1 → MSB

step 2 Write the remainders from MSB to LSB provide the equivalent binary number

1100000