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Answers
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).