Number Storage

• What number system do computer systems use to process data?

  Binary
• What is a bit?

  A single 0 or 1
• How many bits are in a byte?

  8 bits
• What does it mean that binary is a base 2 number system?

  It has 2 possible values: 0 and 1
• What is denary also known as?

  Decimal
• How many possible values does the denary system have?

  10 possible values: 0 to 9
• What is hexadecimal?

  A base 16 number system
• How many possible values does the hexadecimal system have?

  16 possible values: 0 to F
• Why is hexadecimal used as shorthand for binary?

  It uses fewer characters to write values
• What is the hexadecimal equivalent of the binary number 100111101011?

  9EB
• What happens when you convert double-digit numbers in hexadecimal?

  They are converted into letters
• What is the process to convert from denary to hexadecimal?

  Convert to binary first
• What is the process to convert from hexadecimal to denary?

  Convert to binary first
• What is the largest number that can be held in a byte?

  255
• What is an overflow error?

  When a binary value exceeds storage capacity
• What is the effect of shifting left in binary?

  It multiplies the number
• What is the effect of shifting right in binary?

  It divides the number
• What is the effect of shifting left by 2 places?

  Multiplies by 4
• What is the effect of shifting right by 3 places?

  Divides by 8
• What are the steps to convert binary to denary?

  1. Write down the binary number.
  2. Assign powers of 2 from right to left.
  3. Add the values of the bits that are 1.
• What are the steps to convert denary to binary?

  1. Divide the denary number by 2.
  2. Record the remainder.
  3. Repeat until the quotient is 0.
  4. Read the remainders in reverse order.
• What are the steps to convert binary to hexadecimal?

  1. Group binary digits in sets of 4.
  2. Convert each group to its hexadecimal equivalent.
• What are the steps to convert hexadecimal to binary?

  1. Convert each hexadecimal digit to a 4-bit binary equivalent.
  2. Combine the binary values.
• What are the effects of binary shifts?

  • Left shift: multiplies by 2 for each place
  • Right shift: divides by 2 for each place
• What is the effect of shifting right by 2 places?

  Divides by 4
• What is the effect of shifting left by 1 place?

  Multiplies by 2
• What is the effect of shifting left by 3 places?

  Multiplies by 8
• What is the effect of shifting right by 4 places?

  Divides by 16
• What are common exam questions related to number systems?

  • Converting denary to hexadecimal
  • Converting hexadecimal to denary
• What should you practice for number systems exams?

  • Conversions between binary, denary, and hexadecimal
• What is the importance of binary addition?

  • Allows adding binary values directly
  • Avoids conversion to denary
• What is the significance of overflow errors in binary addition?

  • Indicates exceeding storage capacity
  • Important for understanding limits of binary values