An Arithmetic Logic Unit (ALU) is a digital circuit that performs arithmetic and logical operations on binary numbers, essential for CPUs, GPUs, and other computing circuits. Proposed by John von Neumann in 1945, ALUs can handle fixed-point and floating-point operations, and their design can range from simple 1-bit operations to complex functions like multiply-accumulate. The ALU processes data using a specific numeric format, typically two's complement, to facilitate efficient calculations.

2. Topic : Arithmetic Logic operation (ALU)
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3. Arithmetic logic unit
• An arithmetic logic unit (ALU) is a digital electronic circuit
that performs arithmetic and bitwise logical operations on
integer binary numbers.
• This is in contrast to a floating-point unit (FPU), which
operates on floating point numbers. It is a fundamental
building block of many types of computing circuits, including
the central processing unit (CPU) of computers, FPUs, and
graphics processing units.
• A single CPU, FPU or GPU may contain multiple ALUs.

4. History Of ALU
• Mathematician John von Neumann proposed the ALU concept in
1945 in a report on the foundations for a new computer called the
EDVAC(Electronic Discrete Variable Automatic Computer).

5. Typical Schematic Symbol of an ALU
A and B: the inputs to the ALU
R: Output or Result
F: Code or Instruction from the
Control Unit
D: Output status; it indicates cases

6. Circuit operation
• An ALU is a combinational logic circuit
• Its outputs will change asynchronously in
response to input changes
• The external circuitry connected to the ALU is
responsible for ensuring the stability of ALU
input signals throughout the operation.

7. ALU Operations
• 1. Fixed point operations
• 2. Floating point operations

8. Fixed Point (Integer) ALU Operations
• Add
• Add with carry AND
• Subtract
• Multiply
• Subtract with Borrow
• Divide Unsigned Divide
• OR
• XOR
• NOT
• L-Shift
• R-Shift

9. Floating Point ALU Operations
• F add
• F sub
• F Mul
• F Div

10. Functions
• 3 types of functions-
Arithmetic operations
Bitwise logical operations
Bit shift operations

11. Complex operations
• ALU can be designed to perform complex functions
• MAC(Multiply–accumulate operation)
the multiply–accumulate operation is a common
step that computes the product of two numbers and adds
that product to an accumulator
The MAC operation modifies an accumulator a:
• FMA
• FMAC
• VLIW operations

12. A 1-Bit ALU
The logical operations are easiest, because they map directly onto
the hardware components.
The 1-bit logical unit for AND and OR looks like figure
below. The multiplexor on the right then selects a AND b or a
OR b, depending on whether the value of Operation is 0 or 1.
The line that controls the multiplexor is shown in color to
distinguish it from the lines containing data. In the figure
below control and output lines of the multiplexor were
renamed to names that reflect the function of the ALU.

13. A 32-Bit ALU
• 32-bit ALU is created by connecting adjacent “black boxes.” Using xi to mean the
ith bit of x, figure below shows a 32-bit ALU. The adder created by directly linking
the carries of 1-bit adders is called a ripple carry adder.

14. Numerical systems
• An ALU must process numbers using the same format as the
rest of the digital circuit. For modern processors, that almost
always is the two's complement binary number representation.
Early computers used a wide variety of number systems,
including one's complement, sign-magnitude format, and even
true decimal systems, with ten tubes per digit.
• ALUs for each one of these numeric systems had different
designs, and that influenced the current preference for two's
complement, as this is the representation that makes it easier
for the ALUs to calculate additions and subtractions.

15. Practical overview
• Most of a processor's operations are performed
by one or more ALU. An ALU loads data from
input registers, executes, and stores the result
into an output register. A Control Unit tells the
ALU what operation to perform on the data.
Other mechanisms move data between these
registers and memory.