3. Binary Arithmetic

• A byte has how many bits and what is the value of the most significant bit?

  A byte has 8 bits and the value of the most significant bit is 128
• What is the value of the least significant bit in a byte?

  1
• What type of binary shift is used to multiply a binary number?

  Shift all bits to the left
• What type of binary shift is used to divide a binary number?

  Shift all bits to the right
• What specific operation will multiply a binary number by 4?

  Shift all bits two places to the left
• What specific operation will divide a binary number by 2?

  Shift all bits one place to the left
• Binary addition 0 + 0 =?

  0
• Binary addition 0 + 1 =?

  1
• Binary addition 1 + 1 =?

  0 and carry 1
• Binary addition : 1 + 1 + 1 = ?


  1 and carry 1
• Perform a 1-place shift to the left on 0001 0100. What operation has been carried out? (2)

  0010 1000

  Multiplication of 2 , original number was 20 ; new number is 40
• Perform a 1-place shift to the right on 0001 0100

  What operation has been carried out? (2)

  0000 1010

  A division by two
• What is the result of 0100 1011 + 0010 0011?

  0110 1110
• What is the result of 1100 0000 + 1010 0000?


  0010 0000

  1+1 = 0 and carry 1

  but there is no where to put the carry bit. The result is wrong and this is called an overflow error
• What is an overflow error?


  When a calculation or operation produces a result that is too large to be represented within the available memory or data type, it causes an overflow error.
• Explain the problem with an overflow error?


  Exceeding the maximum value that can be stored in a variable or memory space.