SCMP 391 – Homework 9

Appendix A

1. Convert the following numbers to binary: 1984, 4000, 8192.
2. What is 1001101001 (binary) in decimal? In octal? In hexadecimal?
3. Which of the following are valid hexadecimal numbers? BED, CAB, DEAD, DECADE, ACCEDED, BAG, DAD.
4. How many different positive integers can be expressed in k digits using radix r numbers?
5. Perform the following calculations on 8-bit two’s complement numbers. What are the values of each number, and each result, in base 10?
   00101101 11111111 00000000 11110111
+ 01101111 + 11111111 + 11111111 + 11110111
6. How do you add and subtract two numbers in 2’s compliment? Convert the following problems into 8-bit 2’s complement numbers, do them in binary, and convert back. Show your work.
   • 23 + 12 = ?
   • 42 – 16 = ?
   • 17 – 32 = ?
   • -15 + -32 = ?
7. What happens when you try to add the following numbers if represented in two’s complement 8-bit numbers? Show the results in binary, and explain the problem:
   • 65+82 = ?
   • -76+ -88 = ?