Exploring numbers

• The decimal number system uses digits 0 to 9.

  True
• The binary number `1010` is equivalent to decimal 10
• A bit in a binary number represents either 0 or 1.
• The place values in binary are powers of 2.

  True
• What is the binary equivalent of the decimal number 13?

  1101
• What are the place values in the binary number system?

  Powers of 2
• How do you convert a binary number to decimal?

  Multiply by place values and sum
• What is the first step in converting a decimal number to binary?

  Divide by 2 and record remainder
• Steps for decimal to binary conversion

  1️⃣ Divide the decimal number by 2 and record the remainder (0 or 1).

  2️⃣ Divide the result from step 1 by 2 and record the new remainder.

  3️⃣ Repeat step 2 until the result is 0.

  4️⃣ The binary number is formed by writing the remainders in reverse order.
• In binary to decimal conversion, you multiply each bit by its corresponding place value
• The digits used in the hexadecimal number system include 0-9 and A-F.

  True
• Steps for decimal to hexadecimal conversion

  1️⃣ Divide the decimal number by 16 and record the remainder (0-F).

  2️⃣ Divide the result from step 1 by 16 and record the new remainder.

  3️⃣ Repeat step 2 until the result is 0.

  4️⃣ The hexadecimal number is formed by writing the remainders in reverse order.
• When converting a decimal number to hexadecimal, the first step is to divide the number by 16
• To convert a hexadecimal number to decimal, you multiply each digit by its corresponding place value
• Binary is essential for computers because it uses only two digits, 0 and 1.


  True
• The hexadecimal number system has a base of 16 and uses digits 0-9 and A-F.

  True
• Steps to convert a decimal number to binary

  1️⃣ Divide the decimal number by 2 and record the remainder

  2️⃣ Divide the result from step 1 by 2 and record the new remainder

  3️⃣ Repeat step 2 until the result is 0

  4️⃣ The binary number is formed by writing the remainders in reverse order
• Steps for decimal to binary conversion

  1️⃣ Divide the decimal number by 2 and record the remainder (0 or 1)

  2️⃣ Divide the result from step 1 by 2 and record the new remainder

  3️⃣ Repeat step 2 until the result is 0

  4️⃣ Write the remainders in reverse order
• Steps for decimal to binary conversion

  1️⃣ Divide the decimal number by 2 and record the remainder (0 or 1)

  2️⃣ Divide the result from step 1 by 2 and record the new remainder

  3️⃣ Repeat step 2 until the result is 0

  4️⃣ Write the remainders in reverse order
• Match the binary digit with its place value in a binary number system.

  1 ↔️ Power of 2

  0 ↔️ No contribution
• The hexadecimal number system has a base of 16.


  True
• Match the number system with its base.

  Binary ↔️ 2

  Decimal ↔️ 10

  Hexadecimal ↔️ 16
• The decimal number 6719 is equal to 1A3F in hexadecimal.


  True
• What are the place values in the hexadecimal system based on powers of 16?

  1, 16, 256, 4096, etc.
• What is the first step in converting a hexadecimal number to decimal?

  Identify place values
• What is the base of the binary number system?

  2
• How do you convert a binary number to decimal?

  Multiply by place values
• What are the two digits used in the binary number system?

  0 and 1
• The hexadecimal number system has a base of 16
• The binary representation of 13 is 1101
• Bit width refers to the number of bits used to store a number in computer memory
• What is the base of the binary number system?

  2
• What are the place values in the binary number system based on?

  Powers of 2
• Why do computers use binary numbers?

  Two distinct states
• What is the decimal equivalent of the binary number `1101`?

  13
• Steps for decimal to binary conversion:

  1️⃣ Divide the decimal number by 2 and record the remainder.

  2️⃣ Divide the result by 2 and record the new remainder.

  3️⃣ Repeat until the result is 0.

  4️⃣ Form the binary number by writing remainders in reverse order.
• Match the properties of the binary and decimal number systems with their values:

  Base of binary ↔️ 2

  Digits in binary ↔️ 0, 1

  Place values in binary ↔️ Powers of 2

  Base of decimal ↔️ 10

  Digits in decimal ↔️ 0-9

  Place values in decimal ↔️ Powers of 10
• Computers use binary because it is the simplest way to represent data electronically using two distinct states: on and off.

  True
• The first step in converting a decimal number to binary is to divide it by 2
• What are the place values in the binary number system used for binary to decimal conversion?

  Powers of 2