4.3 Other Bases 193 TECHNOLOGY TIP Converting Numerals Apps There are several apps available for use on most smartphones and tablets that can convert numerals between base 10 and other bases. There are also some apps available that convert Roman, Babylonian, and Mayan numerals to and from base 10 numerals. Although these apps can be helpful to convert numerals between bases and numerals from one numeration system to another, be careful to understand if there are any limitations before using such an app. For example, some apps will not convert to and from Roman numerals whose value is greater than 9999. Finally, as always, check with your instructor prior to using any apps to complete required work for your course. Instructor Resources for Section 4.3 in MyLab Math • Objective-Level Videos 4.3 • Interactive Concept Video: Binary and Hexadecimal Numbers • PowerPoint Lecture Slides 4.3 • MyLab Exercises and Assignments 4.3 Exercises Warm Up Exercises In Exercises 1– 4, fill in the blanks with an appropriate word, phrase, or symbol(s). 1. In the numeral 234 ,5 the 5 is called the ________. Base 2. In the numeral 234 ,5 the 2 represents 2 × ________. 52 or 25 3. In the numeral 234 ,5 the 3 represents 3 × ________. 5 4. Computers and other electronic devices make use of the following numeration systems: a) base 2, also called ________. Binary b) base 8, also called ________. Octal c) base 16, also called ________. Hexadecimal Practice the Skills In Exercises 5–22, convert the given numeral to a numeral in base 10. 5. 224 10 6. 314 13 7. 4126 152 8. 5236 195 9. 2418 161 10. 7658 501 11. 30912 441 12. 100512 1733 13. 57316 1395 14. 42316 1059 15. 1101012 53 16. 11101112 119 17. 76548 4012 18. 50328 2586 19. A9112 1549 20. B5212 1646 21. C67916 50,809 22. D20E16 53,774 In Exercises 23–36, convert each of the following to a numeral in the base indicated. 23. 7 to base 2 1112 24. 11 to base 2 10112 25. 5 to base 2 1012 26. 10 to base 2 10102 27. 143 to base 4 20334 28. 591 to base 4 210334 29. 102 to base 5 4025 30. 304 to base 5 22045 31. 1098 to base 8 21128 32. 2921 to base 8 55518 33. 9004 to base 12 526412 34. 6652 to base 12 3A2412 35. 9455 to base 16 24EF16 36. 39,885 to base 16 9BCD16 In Exercises 37– 44, convert 2025 to a numeral in the base indicated. 37. 3 22100003 38. 4 1332214 39. 5 311005 40. 6 132136 41. 7 56227 42. 9 27009 43. 12 120912 44. 16 7E916 Problem Solving In Exercises 45– 48, assume the numerals given are in a base 5 numeration system. Assume the numerals in this system and their equivalent Hindu–Arabic numerals are 5 0 5 1 5 2 5 3 5 4 Write each of the following numerals as a base 10 HinduArabic numeral. 45. 5 13 46. 5 23 47. 5 78 48. 5 73 In Exercises 49–52, write the Hindu–Arabic numerals in the numeration system discussed in Exercises 45– 48. 49. 19 * 50. 23 * 51. 74 * 52. 85 * SECTION 4.3 *See Instructor Answer Appendix
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