Binary numbers

• What must all data be converted into for processing by computers?

  Binary
• Why do computers use binary numbers?

  Because they only understand 1s and 0s
• What is the standard number system used by computers?

  Binary
• How does counting in binary compare to counting in denary?

  • Binary uses two digits: 0 and 1
  • Denary uses ten digits: 0-9
  • Counting in binary is similar to denary
• What are the digits used in the denary number system?

  0, 1, 2, 3, 4, 5, 6, 7, 8, 9
• What is denary also known as?

  Base-10
• What digits does binary use?

  0 and 1
• How does counting in binary differ from counting in denary?

  • Binary increases by powers of 2
  • Denary increases by powers of 10
  • Place values in binary are from right to left
• What is the largest value represented by an 8-bit binary number?

  255
• What is the significance of the left-most bit in binary?

  It is the most significant bit
• What is the least significant bit in binary?

  The right-most bit
• What are the advantages of binary numbers over denary numbers?

  • Easier for computers to process
  • Simplifies electronic circuitry
  • Reduces error in data representation
• How would you convert the binary number $00110101$ to denary?


  53
• What is the process of converting binary to denary?

  1. Write down the binary number
  2. Assign powers of 2 from right to left
  3. Multiply each bit by its power of 2
  4. Sum the results
• What is the binary equivalent of the denary number 10?


  1010
• What does each column in a binary table represent?

  A power of 2
• How do you create a binary table for conversion?

  • List binary place values (1, 2, 4, 8, 16, ...)
  • Write the binary digits under each place value
  • Use the table for conversion to denary
• If you have the binary number $1101$, what is its denary equivalent?


  13
• What is the binary representation of the denary number 255?


  11111111
• Why is binary easier to convert than other number systems?

  It uses only two digits
• What is the method for converting an 8-bit binary number to denary?

  1. Identify each bit's value
  2. Multiply by corresponding power of 2
  3. Sum all values for denary result
• What is the binary equivalent of the denary number 5?

  101
• How do you double a binary number?

  Shift left by one position
• What is the relationship between binary and denary counting?

  Binary is a base-2 system, denary is base-10
• How would you represent the denary number 12 in binary?

  1100
• What is the significance of the binary number system in computing?

  • Fundamental for data representation
  • Basis for computer architecture
  • Essential for programming and algorithms
• What is the binary number given in the study material?


  00110101
• How do you convert an 8-bit binary number to a denary number?

  Each column is a power of 2
• What is the process to convert binary to denary?

  • Draw a table with binary place values
  • Start with 1 at the right, then move left, doubling each time
  • Write the binary number in the table
  • Sum the values of the columns with 1s
• What is the denary equivalent of the binary number 00110101?

  53
• What does the process of doubling each time refer to in binary conversion?

  It refers to the powers of 2 in columns
• What are the steps to convert denary to binary?

  1. Draw a table of binary place values
  2. Subtract the largest binary value from the denary number
  3. Mark the column with a 1, others with 0
  4. Repeat until the denary number is zero
• If you convert the denary number 79 to binary, what is the result?

  01001111
• What is the binary representation of the denary number 79?

  01001111
• What is the significance of the number 19 in the conversion process?

  • It is the value that gives a negative answer
  • It is used to determine the binary representation
  • It helps in the subtraction process during conversion
• What is the final binary number for 79 after conversion?

  01001111
• What are the alternative methods to convert denary to binary?

  • Choose the method you are most comfortable with
  • Use repeated division by 2
  • Use subtraction of binary place values
• What are the two digits used in binary numbers?

  1 and 0
• What is the result of adding 1 and 1 in binary?

  1 + 1 = 10
• What is the process for adding binary numbers using column addition?

  1. Align binary numbers in columns.
  2. Start from the right and add each column.
  3. Carry over if the sum exceeds 1.