In Figure 1.6 we show how to convert a decimal number into binary by successively dividing by
Question:
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
Step by Step Answer:
a 17 16 1 24 20 10001 in binary b 33 32 1 25 20 100001 ...View the full answer
Fundamentals Of Digital Logic With Verilog Design
ISBN: 9780073380544
3rd Edition
Authors: Stephen Brown, Zvonko Vranesic
