CE1911
Homework

Week 8

  1. Encode the number 4,98510 in binary coded decimal.
  2. Decode the number 00101001 10010111 as a binary coded decimal number.
  3. Is 11111010 a valid BCD number? Why or why not?
  4. Is 10010111 a valid BCD number? Why or why not?
  5. What is the next BCD number after 01011001?
  6. What is the next BCD number after 01111001 10011001?
  7. How many words can a 3-bit address memory hold? If each word is 5 bits, how many bits can it hold?
  8. How many bytes can a 12-bit address, 24-bit word memory hold? How many KB (SI)? How many KB (JEDEC)?
  9. (optional) Using two 4-bit binary counters with synchronous reset capability and some combinational logic, create a two-decimal-digit BCD counter. (You may assume the counters also have a reset ability). Test your circuit by simulating it on paper counting from 0 through 20.
  10. (just for fun) How many n-bit counters are there? In other words, with n bits, how many state machines can you use that simply move around a ring of states and return to the start? For starters, suppose that all the states are used. Then there are 2^n states. For example, with 2 bits, these states are 00, 01, 10, and 11. But there are several counters, depending on what binary encodings we use for each state. For example, in addition to the binary counter, you could use a Gray counter 00, 01, 10, 11, or a down counter 11, 10, 01, 00. How many other counters are there? Then, suppose you don't have to use all the states. Consider the ring (one-hot) counter: 01, 10. The possiblities are not endless. How many are there?
  11. (just for fun) With so many possible counters, why not make/find your own? What creative binary encodings can you come up with? I know of at least two interesting varieties of counters that we have not discussed in class. Perhaps you can find a third!

Acknowledgement: Many homework problems originally by Dr. Russ Meier