Question

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Answer 1

Answer:

Q 6

(i)  (1101)2 = (13)10

(ii)  (25)10 = (11001)2

Explanation:

Step 1: Write down the binary number:                                        

1101

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

1x2^3 + 1x2^2 + 0x2^11 + 1x2^0

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.

Q6 (ii)

Step 1: Divide (25)10 successively by 2 until the quotient is 0:

25/2 = 12, remainder is 1      

12/2 = 6, remainder is 0      ↑

6/2 = 3, remainder is 0       ↑

3/2 = 1, remainder is 1         ↑

1/2 = 0, remainder is 1         ↑

Step 2: Read from the bottom (MSB) to top (LSB) as 11001. This is the binary equivalent of decimal number 25 (Answer).