# EXERCISES
###### tags: `Computer Science `

## Chapter 2 Binary Values and Number Systems
For Exercises 1–5, match the following numbers with their definition.
A. Number
B. Natural number
C. Integer number
D. Negative number
E. Rational number
1. A unit of an abstract mathematical system subject to the laws of
arithmetic
2. A natural number, a negative of a natural number, or zero
3. The number zero and any number obtained by repeatedly adding one
to it
4. An integer or the quotient of two integers (division by zero excluded)
5. A value less than zero, with a sign opposite to its positive counterpart
For Exercises 6–11, match the solution with the problem.
A. 10001100
B. 10011110
C. 1101010
D. 1100000
E. 1010001
F. 1111000
6. 1110011 + 11001 (binary addition)
7. 1010101 + 10101 (binary addition)
8. 1111111 + 11111 (binary addition)
9. 1111111 – 111 (binary subtraction)
10. 1100111 – 111 (binary subtraction)
11. 1010110 – 101 (binary subtraction)
For Exercises 12–17, mark the answers true or false as follows:
A. True
B. False
12. Binary numbers are important in computing because a binary number
can be converted into every other base.
13. Binary numbers can be read off in hexadecimal but not in octal.
14. Starting from left to right, every grouping of four binary digits can be
read as one hexadecimal digit.
15. A byte is made up of six binary digits.
16. Two hexadecimal digits cannot be stored in one byte.
17. Reading octal digits off as binary produces the same result whether
read from right to left or from left to right.
Exercises 18–47 are problems or short-answer questions.
18. Distinguish between a natural number and a negative number.
19. Distinguish between a natural number and a rational number.
20. Label the following numbers as natural, negative, or rational.
a. 1.333333
b. –1/3
c. 1066
d. 2/5
e. 6.2
f. π (pi)
21. How many ones are there in 891 if it is a number in each of the following bases?
a. Base 10
b. Base 8
c. Base 12
d. Base 13
e. Base 16
22. Express 891 as a polynomial in each of the bases in Exercise 21.
23. Convert the following numbers from the base shown to base 10.
a. 111 (base 2)
b. 777 (base 8)
c. FEC (base 16)
d. 777 (base 16)
e. 111 (base 8)
24. Explain how base 2 and base 8 are related.
25. Explain how base 8 and base 16 are related.
26. Expand the table on page 43 to include the decimals from 11 through 16.
27. Expand the table in Exercise 26 to include hexadecimal numbers.
28. Convert the following binary numbers to octal.
a. 111110110
b. 1000001
c. 10000010
d. 1100010
29. Convert the following binary numbers to hexadecimal.
a. 10101001
b. 11100111
c. 01101110
d. 01121111
30. Convert the following hexadecimal numbers to octal.
a. A9
b. E7
c. 6E
31. Convert the following octal numbers to hexadecimal.
a. 777
b. 605
c. 443
d. 521
e. 1
32. Convert the following decimal numbers to octal.
a. 901
b. 321
c. 1492
d. 1066
e. 2001
33. Convert the following decimal numbers to binary.
a. 45
b. 69
c. 1066
d. 99
e. 1
34. Convert the following decimal numbers to hexadecimal.
a. 1066
b. 1939
c. 1
d. 998
e. 43
35. If you were going to represent numbers in base 18, which symbols might you use to represent the decimal numbers 10 through 17 other than letters?
36. Convert the following decimal numbers to base 18 using the symbols you suggested in Exercise 35.
a. 1066
b. 99099
c. 1
37. Perform the following octal additions.
a. 770 + 665
b. 101 + 707
c. 202 + 667
38. Perform the following hexadecimal additions.
a. 19AB6 + 43
b. AE9 + F
c. 1066 + ABCD
39. Perform the following octal subtractions.
a. 1066 – 776
b. 1234 – 765
c. 7766 – 5544
40. Perform the following hexadecimal subtractions.
a. ABC – 111
b. 9988 – AB
c. A9F8 – 1492
41. Why are binary numbers important in computing?
42. How many bits does a byte contain?
43. How many bytes are there in a 64-bit machine?
44. Why do microprocessors such as pagers have only 8-bit words?
45. Why is it important to study how to manipulate fixed-size numbers?
46. How many ones are there in the number AB98 in base 13?
47. Describe how a bi-quinary number representation works.