Computer Architecture and Organisation

Topic 5: The Arithmetic Logic Unit

• Arithmetic Logic Unit (ALU)
  

  The arithmetic logic unit (ALU) is a part of computer that performs arithmetic and bitwise operations on integer binary numbers which contrast to a floating-point unit (FPU) that operates on floating point numbers. It consists of combinational digital electronic circuit that becomes a fundamental building block of many types of computing circuits, including the central processing unit (CPU) of computers.

  

  
  

  BINARY HALF-ADDER

  
  

  The binary half adder is a logic circuit (Figure 5.29) that has 2 inputs; A and B that added together. It has two outputs; sum (S) and carry (C). The value of the sum in decimal system is 2C + S. The carry signal represents an overflow into the next digit of a multi-digit addition.

  

  
  

  The simplest half-adder incorporates an XOR gate for S and an AND gate for C. With the addition of an OR gate to combine their carry outputs, two half adders can be combined to make a full adder.

  
  

  
  

  The half-adder truth table is as shown in Table 5.9 where S= A Å B (Exclusive OR) and C = A.B (AND).

  A	B	Sum	Carry-Out
  0	0	0	0
  0	1	1	0
  1	0	1	0
  1	1	0	1

  
  FULL ADDER

  
  

  The full-adder has 3 inputs; A, B and C_in that adds three one-bit binary numbers. The outputs are 2 one-bit binary numbers, a sum (S) and a carry (C_out). The full-adder is usually a component in a cascade of adders that add 8, 16, 32 binary numbers.
  

  
  

  
  

  
  

  The simplest way to construct a full adder logic diagram is to connect two half- adder and
  an OR gate as shown below. The full-adder is then the fundamental logic
  circuit incorporated in digital computers to perform arithmetic functions.

  
  

  
  

  The full adder truth table is represented in Table 5.10 where S= A Å B Å C_in and C=AB + C_in (A Å B).

  A	B	Carry-In	Sum	Carry-Out
  0	0	0	0	0
  0	0	1	1	0
  0	1	0	1	0
  0	1	1	0	1
  1	0	0	1	0
  1	0	1	0	1
  1	1	0	0	1
  1	1	1	1	1

  
  

  
  

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• Lecture Note Topic 5 - The Arithmetic Logic Unit File

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• Self Check - Topic 5 Lesson

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• Summary

  In this topic you have learnt that:

  The Arithmetic Logic Unit (ALU) construction, binary half-adder, binary full adder, binary coded decimal (BCD), positive and negative BCD, shift operation and high-speed arithmetic.

  
  

  
  

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