Computer Architecture and Organisation

Topic 3: Integers

• Unsigned

  Unsigned represents the positive integers. For example, 157₁₀ can be represented as shown in Table 3.1 below:
  

  Table 3.1
  Position	7	6	5	4	3	2	1	0
  Bit pattern	1	0	0	1	1	1	0	1
  Contribution	27			24	23	22		20

  
  

  

  
  

  BCD NUMBER REPRESENTATION
  

  BCD number representation is a way to express each of the decimal digits with a binary code. In BCD, the decimal digit is represented by a 4-bit binary number. It can represent sixteen numbers (0000 to 1111) however in BCS code, it is only first ten of these are used (000 to 1001). The remaining are invalid in BCD.

  It is shown in Table 3.2:

  

  
  

  
  

  SIGN AND MAGNITUDE
  

  Sign magnitude notation is one of the methods used to represent the negative numbers. In signed magnitude the left-most bit represents the sign of the integer where zero (0) for positive numbers and one (1) for negative numbers. The remaining bits represent magnitude of the numbers.

  Example 1:

  0       0 1 1 0 1 0 1 = +53   Positive   magnitude bits sign

  1       0 1 1 0 1 0 1 = -53    Negative magnitude bits sign

  
  

  Example 2:

  Suppose 10011101₂ is a signed magnitude representation. The sign bit is 1, then the number represented is negative. It can be represented as in Table 3.3:

  Table 3.3
  Position	7	6	5	4	3	2	1	0
  Bit pattern	1	0	0	1	1	1	0	1
  Contribution	-			24	23	22		20

   

  The magnitude is 0011101₂ with a value 2⁴+2³+2²+2⁰= 29₁₀. So, the number represented by 10011101₂ is –29.

  The advantage of signed magnitude representation is it represents positive and negative numbers. The disadvantages of signed magnitude representation; it has two representations of zero and arithmetic operations are difficult. 

  
  

  
  

  Mark as done
• Lecture Note Topic 3 - Integers File

  Mark as done
• Self Check: Integers Quiz

  Restricted Not available unless:

  • The activity UnsignedUnsigned represents the positive integers... is marked complete
  • The activity Lecture Note Topic 3 - Integers is marked complete

  
  

• Summary

  In this topic you have learnt that:

  Unsigned, BCD number representation, sign magnitude, negative numbers, overflow, carry, floating points, format and exponents.

  
  

  
  

  Mark as done