3.3.4 Binary arithmetic

• The binary representation of 25 is 11001
• To convert a binary number to decimal, multiply each digit by its positional value.


  True
• The positional value of the leftmost digit in 11001 is 2^4
• The decimal representation of binary 11001 is 25.


  True
• In binary addition, 1 + 1 equals 10
• Steps to add binary numbers 1010 and 0111

  1️⃣ 0 + 1 = 1

  2️⃣ 1 + 1 = 10 (carry-over 1)

  3️⃣ 0 + 1 + 1 = 10 (carry-over 1)

  4️⃣ 1 + 0 + 1 = 10 (carry-over 1)

  5️⃣ Write the result from right to left
• The sum of 1010 and 0111 in binary is 10001
• What is the result of adding 1 + 1 in binary arithmetic?

  10
• Steps for adding binary numbers in an example

  1️⃣ 0 + 1 = 1 (Carry-over 0)

  2️⃣ 1 + 1 = 10 (Carry-over 1)

  3️⃣ 0 + 1 + 1 = 10 (Carry-over 1)

  4️⃣ 1 + 0 + 1 = 10 (Carry-over 1)
• The binary sum of 1010 and 0111 is 10001.


  True
• What is the carry-over value when adding 1 + 1 in binary arithmetic?

  1
• In binary subtraction, 1 - 0 equals 1.

  True
• In binary subtraction, if the top digit is smaller than the bottom digit, you must borrow 1 from the next column
• What is the result of subtracting 1010 - 0111 in binary arithmetic?

  0101
• The binary difference between 1010 and 0111 is 0101.


  True
• What base does the decimal number system use?

  10
• The binary number system uses base 2
• What decimal number does the binary number 1011 represent?

  11
• In binary subtraction, 1 - 1 equals 0.


  True
• What is the result of subtracting 1010 - 0111 in binary?

  0011
• What is the result of multiplying 1011 and 101 in binary?

  110111
• What is the quotient when 10010 is divided by 101 in binary?

  100
• Steps to divide the binary number 10010 by 101

  1️⃣ 10010 ÷ 101 (Binary) = 18 ÷ 5 (Decimal)

  2️⃣ 101 x 0 = 0

  3️⃣ 10010 - 0 = 10010

  4️⃣ Bring down 0

  5️⃣ 10010 ÷ 101 = 100
• In binary division, the remainder, if any, is written at the end of the division
• In computer programming, binary arithmetic is used to perform calculations and control the flow of programs
• Binary arithmetic is used to encode text, images, audio, and video in data storage.


  True
• Steps for converting a decimal number to binary

  1️⃣ Repeatedly divide by 2

  2️⃣ Keep track of remainders

  3️⃣ Read remainders from bottom to top
• What base does the decimal number system use?

  Base 10
• In the decimal number system, each position represents a positional value equal to 10 raised to the power of its position
• What base does the binary number system use?

  Base 2
• In the binary number system, each position represents a positional value equal to 2 raised to the power of its position
• The binary number 1011 represents the decimal number 11.


  True
• Steps to convert a decimal number to binary

  1️⃣ Divide the decimal number by 2

  2️⃣ Take the remainder

  3️⃣ Repeat until the decimal number is 0

  4️⃣ Write the remainders in reverse order
• To convert a decimal number to binary, divide the decimal number by 2
• When converting from decimal to binary, remainders are taken in reverse order.


  True
• Steps to convert decimal 25 to binary

  1️⃣ Divide 25 by 2

  2️⃣ Record the remainder (1)

  3️⃣ Divide 12 by 2

  4️⃣ Record the remainder (0)

  5️⃣ Repeat until the quotient is 0

  6️⃣ Write the remainders in reverse order
• What is the binary representation of the decimal number 25?

  11001
• The binary number 11001 represents the decimal number 25.


  True
• What is the result of adding 0 + 0 in binary arithmetic?

  0
• In binary arithmetic, 1 + 1 equals 10 with a carry-over of 1.

  True