Decimal (base-10) and binary (base-2)

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Quick Questions

Shade in the A or B circle for each question.

1. Which number system uses the ten digits 0 to 9?

A Decimal (base-10)

B Binary (base-2)

2. Which number system uses only the digits 0 and 1?

A Decimal (base-10)

B Binary (base-2)

3. What does the 'base' of a number system tell you?

A How many different digits the system uses

B How big the largest number can be

4. Your phone shows the price of a game as $25. Which system is this price written in?

A Binary

B Decimal

5. Which system do computers use to store and process data?

A Binary

B Decimal

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
1base-10		ABinary only has two digits, 0 and 1. The digit 2 does not exist in binary.
2base-2		BThe decimal system, which uses ten different digits: 0 to 9
3Everyday numbers like prices and scores are written in decimal, using digits 0 to 9		CThe binary system, which uses only two different digits: 0 and 1
4Computers store numbers using only two digits, so they use binary		DBinary: 0 1
5Binary (base-2) digits: 0 1 2		EDecimal is base-10 and uses ten digits, 0 to 9. Base-2 is binary.
6Decimal is base-2 and uses 0 and 1		FDecimal: 0 1 2 3 4 5 6 7 8 9

Definitions

decimal base-10, binary base-2

Fill in the Blanks

Complete each line of code by filling in the missing parts.

decimalBase ← __

binaryBase ← _

FOR digit ← 0 TO _ DISPLAY digit END FOR

base ← 2 IF ____ = 2 THEN DISPLAY "binary"

Spot the Error

Shade in the letter of the line that contains an error.

Question 1

A decimal_base = 2

B binary_base = 2

C print(decimal_base)

Question 2

A decimal_digits = "0123456789"

B binary_digits = "01"

C binary_base = len(decimal_digits)

Question 3

A computers_use = "decimal"

B people_use = "decimal"

C print(computers_use, "is base-2")

Question 4

A bits = ["0", "1"]

B base = len(bits)

C print("Binary is base", base)

D print("Computers use decimal")

Question 5

A digits = "0123456789"

B base = len(digits) - 1

C print("Base", base)

Answer Key

Decimal (base-10) and binary (base-2)

Section A: Quick Questions

A — Decimal (base-10)

B — Binary (base-2)

A — How many different digits the system uses

B — Decimal

A — Binary

Section B: Match the Pairs

base-10 → The decimal system, which uses ten different digits: 0 to 9

base-2 → The binary system, which uses only two different digits: 0 and 1

Everyday numbers like prices and scores are written in decimal, using digits 0 to 9 → Decimal: 0 1 2 3 4 5 6 7 8 9

Computers store numbers using only two digits, so they use binary → Binary: 0 1

Binary (base-2) digits: 0 1 2 → Binary only has two digits, 0 and 1. The digit 2 does not exist in binary.

Decimal is base-2 and uses 0 and 1 → Decimal is base-10 and uses ten digits, 0 to 9. Base-2 is binary.

Section C: Definitions

decimal base-10, binary base-2 — Decimal is base-10 and uses ten digits, 0 to 9. Binary is base-2 and uses only 0 and 1. People use decimal every day, but computers use binary.

Section D: Fill in the Blanks

decimalBase ← 10

binaryBase ← 2

FOR digit ← 0 TO 9
  DISPLAY digit
END FOR

FOR digit ← 0 TO 1
  DISPLAY digit
END FOR

base ← 2
IF base = 2 THEN
  DISPLAY "binary"

Section E: Spot the Error

A — Decimal is base-10 because it uses ten digits (0 to 9). Line 1 should be decimal_base = 10. Base 2 belongs to binary.

C — The base is how many different digits a system uses. Binary has only two digits, so binary_base must be len(binary_digits), which is 2. Using decimal_digits would give 10.

A — Computers use binary, not decimal. Line 1 should be computers_use = "binary", which matches the base-2 message on line 3.

D — The program is about binary, which has two digits (base-2) and is what computers use. Line 4 should say "Computers use binary".

B — The base is the number of different digits. Decimal has ten digits (0 to 9), so base = len(digits) gives 10. Subtracting 1 gives 9, which is wrong.