Question

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Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

a)65 Decimal To Binary Conversion:

step 1 Perform the successive MOD operation by 2 for the given decimal number 65 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).

65 / 2 = 32 : Remainder is 1 → LSB

32 / 2 = 16 : Remainder is 0

16 / 2 = 8 : Remainder is 0

8 / 2 = 4 : Remainder is 0

4 / 2 = 2 : Remainder is 0

2 / 2 = 1 : Remainder is 0Step

b )1) Divide 657 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 657 as a binary.

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

657 / 2 = 328 with 1 remainder

328 / 2 = 164 with 0 remainder

164 / 2 = 82 with 0 remainder

82 / 2 = 41 with 0 remainder

41 / 2 = 20 with 1 remainder

20 / 2 = 10 with 0 remainder

10 / 2 = 5 with 0 remainder

5 / 2 = 2 with 1 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 657 converted to binary is therefore:

1010010001

1 / 2 = 0 : Remainder is 1 → MSB

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

1000001

6510 = 10000012

Q.2

a)Step by step solution

Step 1: Write down the binary number:

1011

Step 2: Multiply each digit of the binary number by the corresponding power of two:

1x23 + 0x22 + 1x21 + 1x20

Step 3: Solve the powers:

1x8 + 0x4 + 1x2 + 1x1 = 8 + 0 + 2 + 1

Step 4: Add up the numbers written above:

8 + 0 + 2 + 1 = 11.

So, 11 is the decimal equivalent of the binary number 1011.

b)Step by step solution

Step 1: Write down the binary number:

10101

Step 2: Multiply each digit of the binary number by the corresponding power of two:

1x24 + 0x23 + 1x22 + 0x21 + 1x20

Step 3: Solve the powers:

1x16 + 0x8 + 1x4 + 0x2 + 1x1 = 16 + 0 + 4 + 0 + 1

Step 4: Add up the numbers written above:

16 + 0 + 4 + 0 + 1 = 21.

So, 21 is the decimal equivalent of the binary number 10101.