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Chapter 1: Number Bases: Value of The Digit

This document contains a chapter on number bases that includes: 1) Converting numbers between different number bases, such as binary, octal, decimal, and pentinary. 2) Performing arithmetic operations like addition and subtraction in different number bases. 3) Determining the value of digits in multi-place numbers of varying bases. The chapter provides practice problems for students to gain experience working with and converting between different number base systems.

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Jiajia Lau
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135 views7 pages

Chapter 1: Number Bases: Value of The Digit

This document contains a chapter on number bases that includes: 1) Converting numbers between different number bases, such as binary, octal, decimal, and pentinary. 2) Performing arithmetic operations like addition and subtraction in different number bases. 3) Determining the value of digits in multi-place numbers of varying bases. The chapter provides practice problems for students to gain experience working with and converting between different number base systems.

Uploaded by

Jiajia Lau
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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CHAPTER 1: NUMBER BASES

A. Write each of the following numbers in expanded notation.


1. 1012 2. 345 3. 7328

B. Convert the following numbers to number in base ten.


1. 10012 2. 101012 3. 110012
4. 111112 5. 110112 6. 2115
7. 1045 8. 3125 9. 10225
10. 10015 11. 548 12. 608
13. 2628 14. 1008 15. 328
C. Determine the value of the underlined digit, in base ten, for the following numbers.
1. 1 1 1 0 0 12 2. 1 0 1 0 12 3. 1 1 0 0 12
Value of the digit =
4. 3 2 0 15 5. 4 3 25 6. 1 0 1 15
7. 1 0 2 48 8. 7 2 38 9. 4 0 0 25

D. Convert the following numbers to numbers in the stated base.


1. 15 → base 2 2. 24 → base 2 3. 145 → base 2

4. 100 → base 2 5. 54 → base 2 6. 72 → base 2

7. 68 → base 8 8. 90 → base 8 9. 1005 → base 8

10. 465 → base 8 11. 233 → base 8 12. 1214 → base 8

13. 23 → base 5 14. 34 → base 5 15. 90 → base 5


16. 102 → base 5 17. 231 → base 5 18. 175 → base 5

19. 55 → base 5 20. 83 → base 5

E. Convert each of the following numbers to number in stated base.


1. 158 → base 2 2. 248 → base 2 3. 1458 → base 2

4. 1110102 → base 8 5. 11000002 → base 8 6. 1000012 → base 8

7. 11012 → base 5 8. 1100112 → base 5 9. 11002 → base 5

10. 4658 → base 5 11. 348 → base 5 12. 178 → base 5


13. 1025 → base 2 14. 215 → base 2 15. 175 → base 2

16. 345 → base 8 17. 435 → base 8 18. 1005 → base 8

F. Calculate each of the following and state your answers in base two.
Addition Subtraction
02 + 02 = 02 02 − 02 = 02
12 + 02 = 12 12 − 02 = 12
12 + 12 = 102 12 − 12 = 02
102 + 12 = 112 102 − 12 =12
12 + 12 +12 = 112 112 − 12 =102

1. 11012  112  2. 1100 2  1111 2  3. 1012  10012 

4. 112  11000 2  5. 110012  1012  6. 11012  10 2 

7. 110012  100 2  8. 11000 2  10012  9. 10100 2  1000 2 

G. Convert each of the following numbers to number in base eight.

NOTA PENTING:
Base 2 000 001 010 011 100 101 110 111
Base 8 0 1 2 3 4 5 6 7

1. 11012 2. 11011 2 3. 10111 2 

4. 11000 2  5. 11010 2  6. 10012 

H. State each of the following as a number in base two, eight or five.


1. 24 + 23 + 2 (Base 2) 2. 25 + 23 (Base 2)
3. 25 + 24 + 22 + 1 (Base 2) 4. 26 + 2 + 1 (Base 2)

5. 2(23 + 22 + 1) (Base 2) 6. 2(25 + 4) (Base 2)

7. 2╳53 + 4╳52 + 5 (Base 5) 8. 3╳54 + 52 + 4╳5 + 1 (Base 5)

9. 54 + 2╳52 + 2╳5 +3 (Base 5) 10. 52 + 2 (Base 5)

11. 5(53 + 52 + 5) (Base 5) 12. 5(52 + 3) (Base 5)

13. 84╳2 +83╳5 + 82 + 7 (Base 8) 14. 83╳5 + 82╳3 + 4 (Base 8)

15. 8(82 + 1) (Base 8) 16. 83 + 3 (Base 8)

Enrichment exercise: Answer all the questions.

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