In Figure 1.6 we show how to convert a decimal number into binary by successively dividing by 2. Another way to derive the answer is to construct the number by using powers of 2. For example, if we wish to convert the number (23)₁₀, then the largest power of 2 that is not larger than 23 is 24 = 16. Hence, the binary number will have five bits and the most significant bit is b₄ = 1. We then perform the subtraction 23 − 16 = 7. Now, the largest power of 2 that is not larger than 7 is 2² = 4. Hence, b₃ = 0 (because 2³ = 8 is larger than 7) and b₂ = 1. Continuing this process gives

23 = 16 + 4 + 2 + 1
      = 2⁴ + 2² + 2¹ + 2⁰
      = 10000 + 00100 + 00010 + 00001
      = 10111

Using this method, convert the following decimal numbers into binary.
(a) (17)₁₀
(b) (33)₁₀
(c) (67)₁₀
(d) (130)₁₀
(e) (2560)₁₀
(f) (51200)₁₀

Convert (857) 10 857 + 2 = 428 2 214 + 2 107 + 2 53 2 26 + 2 13 + 2 6+ 2 3+2 1 + 2 = 428 214 107 53 26 13 6 3 1 0 Remainder 1 0 0 1 1 0 1 0 1 1 LSB MSB Result is (1101011001).