Topic : Arithmetic Logic operation (ALU)

Prepared by Group Unpredictable

Group Members:

ID NAME

13203015 Mustafa kamal

13203021 Ashikuzzaman

13203065 Towhedul Islam

13203061 Md Monem Rafat Hussain

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.

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).

Typical Schematic Symbol of an ALU

A and B: the inputs to the ALUR: Output or Result F: Code or Instruction from theControl Unit D: Output status; it indicates cases

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.

ALU Operations

• 1. Fixed point operations

• 2. Floating point operations

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

Floating Point ALU Operations

• F add

• F sub

• F Mul

• F Div

Functions

• 3 types of functions-

Arithmetic operations

Bitwise logical operations

Bit shift operations

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

A 1-Bit ALUThe 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.

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.

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.

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.