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Numeration Systems
19 questions By Tony R. Kuphaldt
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Question 10 of 19
Explain why binary is a natural numeration system for expressing numbers in electronic circuits. Why not decimal or some other base of numeration?
How do you suspect binary numbers may be stored in electronic systems, for future retrieval? What advantages are there to the use of binary numeration in storage systems?
Reveal answerThe two states of an on/off circuit are equivalent to 0 and 1 ciphers in binary. Any medium in which on/off states may be physically represented is applicable to storing binary numbers. Optical disks (CD-ROM, DVD) are an excellent example of this, with laser-burned “pits” representing binary bits.
Notes:Ask your students to think of different media or physical quantities which may represent binary information, especially those related to electric/electronic circuits.
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Question 11 of 19
Convert the following numbers from binary (base-two) to decimal (base-ten):
- 102 =
- 10102 =
- 100112 =
- 111002 =
- 101112 =
- 1010112 =
- 111001102 =
- 100011010112 =
Describe a general, step-by-step procedure for converting binary numbers into decimal numbers.
Reveal answer- 102 = 210
- 10102 = 1010
- 100112 = 1910
- 111002 = 2810
- 101112 = 2310
- 1010112 = 4310
- 111001102 = 23010
- 100011010112 = 113110
Notes:The most important part of this question, of course, is the method of translating binary into decimal. Don’t tell your students how to do this, as there are plenty of good references to be found on the procedure. If a student cannot research and understand how to convert binary into decimal without your help, they aren’t trying hard enough!
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Question 12 of 19
Convert the following numbers from decimal (base-ten) to binary (base-two):
- 710 =
- 1010 =
- 1910 =
- 25010 =
- 51110 =
- 82410 =
- 104410 =
- 924110 =
Describe a general, step-by-step procedure for converting decimal numbers into binary numbers.
Reveal answer- 710 = 1112
- 1010 = 10102
- 1910 = 100112
- 25010 = 111110102
- 51110 = 1111111112
- 82410 = 11001110002
- 104410 = 100000101002
- 924110 = 100100000110012
Notes:The most important part of this question, of course, is the method of translating decimal into binary. Don’t tell your students how to do this, as there are plenty of good references to be found on the procedure. If a student cannot research and understand how to convert decimal into binary without your help, they aren’t trying hard enough!
