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1
A Simple ALU
Binary Logic
Page 2


1
A Simple ALU
Binary Logic
2
Outline
l Binary Logic
l Representation of Logic Gates
l Constructing a 1-bit adder
l Constructing an n-bit adder
Page 3


1
A Simple ALU
Binary Logic
2
Outline
l Binary Logic
l Representation of Logic Gates
l Constructing a 1-bit adder
l Constructing an n-bit adder
3
Binary Logic
l A computer works using digital electronics.
l There are only High and Low voltages
l All computer logic is based on the
manipulation of these
l Abstractly,
» High is interpreted as 1 (true)
» Low is interpreted as 0 (false)
Page 4


1
A Simple ALU
Binary Logic
2
Outline
l Binary Logic
l Representation of Logic Gates
l Constructing a 1-bit adder
l Constructing an n-bit adder
3
Binary Logic
l A computer works using digital electronics.
l There are only High and Low voltages
l All computer logic is based on the
manipulation of these
l Abstractly,
» High is interpreted as 1 (true)
» Low is interpreted as 0 (false)
4
Logic Circuit
l A logic circuit takes in a number of input
lines (A, B, C, ...)
» and has a number of output lines (X,Y,Z,...)
A
B
C
X
Y
Z
Page 5


1
A Simple ALU
Binary Logic
2
Outline
l Binary Logic
l Representation of Logic Gates
l Constructing a 1-bit adder
l Constructing an n-bit adder
3
Binary Logic
l A computer works using digital electronics.
l There are only High and Low voltages
l All computer logic is based on the
manipulation of these
l Abstractly,
» High is interpreted as 1 (true)
» Low is interpreted as 0 (false)
4
Logic Circuit
l A logic circuit takes in a number of input
lines (A, B, C, ...)
» and has a number of output lines (X,Y,Z,...)
A
B
C
X
Y
Z
5
Logic Basics
l Every expression evaluates to 1  or 0
l NOT
» ~A (“A bar”)
– is the complement of A,   i.e. 1-A
l OR
» A + B
– is 1 if and only if at least one of A or B is 1, else 0
l AND
» A.B
– is 1 if and only if both A and B are 1, else 0
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FAQs on PPT: A Simple ALU (Binary Logic) - GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

1. What is an ALU in binary logic?
An ALU (Arithmetic Logic Unit) in binary logic is a digital circuit that performs arithmetic and logical operations on binary numbers. It is a key component of the central processing unit (CPU) in a computer and is responsible for executing arithmetic calculations like addition, subtraction, multiplication, and logical operations such as AND, OR, and NOT.
2. How does an ALU operate in binary logic?
An ALU in binary logic operates by receiving two binary numbers as inputs and performs the desired arithmetic or logical operation based on control signals. It uses various logic gates, such as AND, OR, XOR, and NOT gates, to manipulate the binary data. The ALU then produces the result of the operation as an output, which can be further used in the computer's processing.
3. What are the key components of a simple ALU in binary logic?
The key components of a simple ALU in binary logic include: 1. Arithmetic circuit: This circuit performs arithmetic operations like addition and subtraction on the binary numbers. 2. Logic circuit: This circuit executes logical operations such as AND, OR, and NOT on the binary inputs. 3. Control unit: The control unit generates control signals to direct the ALU's operations based on the desired arithmetic or logical operation. 4. Multiplexers: These components select the inputs and outputs based on the control signals. 5. Registers: Registers store intermediate results and facilitate the flow of data within the ALU.
4. What are the applications of ALU in binary logic?
ALUs find applications in various digital systems, including computers, calculators, microcontrollers, and digital signal processors. Some common applications of ALUs in binary logic include: 1. Arithmetic calculations: ALUs perform arithmetic operations needed for calculations in mathematical software and applications. 2. Logical operations: ALUs execute logical operations required for decision-making and control in digital systems. 3. Data manipulation: ALUs are used for data manipulation tasks, such as shifting, rotating, and bit-wise operations. 4. Data encryption and decryption: ALUs play a crucial role in cryptographic algorithms for secure data transmission and storage. 5. Control unit operations: ALUs assist in executing control unit operations, such as comparing values, determining conditions, and branching instructions.
5. How does a simple ALU differ from a complex ALU in binary logic?
A simple ALU in binary logic performs basic arithmetic and logical operations using a limited set of operations and functions. It usually operates on fixed-width binary numbers and has a relatively smaller number of components. On the other hand, a complex ALU in binary logic offers a wider range of arithmetic and logical operations, including more advanced functions like multiplication, division, and square root. It may support variable-width or floating-point numbers and requires a larger number of components to implement the additional operations. Complex ALUs are often found in high-performance processors and specialized digital systems.
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