Question

a. Convert (1101) to decimal.
b.Convert 35 into binary.
c. Add 1011 and 101.
. Calculations must be
shown. ​

Answer 1

Answer:

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Explanation:

1)

(1101)2 = (13)10

Step by step solution

Step 1: Write down the binary number:

1101

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

1x23 + 1x22 + 0x21 + 1x20

Step 3: Solve the powers:

1x8 + 1x4 + 0x2 + 1x1 = 8 + 4 + 0 + 1

Step 4: Add up the numbers written above:

8 + 4 + 0 + 1 = 13. This is the decimal equivalent of the binary number 1101.

2)

Step 1) Divide 35 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 35 as a binary.

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

35 / 2 = 17 with 1 remainder

17 / 2 = 8 with 1 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 35 converted to binary is therefore:

100011

3)

1011

+101

------

10000