Base Number Systems Practice

Base Number Systems

Digits available

Write out the digits used by each of the following number systems.
Do NOT use a lookup table or calculator to determine answers.

Number System	Digits Used
Decimal	?
Binary	?
Hexadecimal	?
Octal	?

Determine in which base number system(s) the following numbers are valid.
The choices for base number systems are (D)ecimal, (B)inary, (H)exadecimal, and (O)ctal.
Do NOT use a lookup table or calculator to determine answers.

Number	Valid Number System?
999	D?, B?, H?, O?
1000	D?, B?, H?, O?
777	D?, B?, H?, O?
11A	D?, B?, H?, O?
2002	D?, B?, H?, O?

Counting

Count from zero to sixteen in each of the following number systems.
Do NOT use a lookup table or calculator to determine answers.

Decimal	Binary	Hexadecimal	Octal
0	?	?	?
1	?	?	?
2	?	?	?
3	?	?	?
4	?	?	?
5	?	?	?
6	?	?	?
7	?	?	?
8	?	?	?
9	?	?	?
10	?	?	?
11	?	?	?
12	?	?	?
13	?	?	?
14	?	?	?
15	?	?	?
16	?	?	?

Column Values

Write both the exponent and actual value (e.g., 10⁰= 1) for the first eight columns of each of the following number systems. The first column has been done for you.
Do NOT use a lookup table or calculator to determine answers.

Decimal
Position	8th	7th	6th	5th	4th	3rd	2nd	1st
Power	?	?	?	?	?	?	?	10⁰
Value	?	?	?	?	?	?	?	1
Binary
Position	8th	7th	6th	5th	4th	3rd	2nd	1st
Power	?	?	?	?	?	?	?	2⁰
Value	?	?	?	?	?	?	?	1
Hexadecimal
Position	8th	7th	6th	5th	4th	3rd	2nd	1st
Power	?	?	?	?	?	?	?	16⁰
Value	?	?	?	?	?	?	?	1
Octal
Position	8th	7th	6th	5th	4th	3rd	2nd	1st
Power	?	?	?	?	?	?	?	8⁰
Value	?	?	?	?	?	?	?	1

Write the decimal value of each of the following numbers.
Do NOT use a lookup table or calculator to determine answers.

	Decimal Value
Binary value 111₂ =	?
Hexadecimal value 15D₁₆ =	?
Octal value 263₈ =	?

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