ARITHMETIC LOGIC UNIT (ALU)
CHAPTER 4
Learning Outcomes
• At the end of this lesson, student should able:-– Understanding adder component in ALU such
as Half Adder, Full Adder, Parallel Binary Adder, Binary Code Decimal Adder etc.
– Understanding shift register operation in ALU– Understanding logical operations in ALU– Realize multiplexer in ALU with eight input
multiplexer.
Introduction
• A logic circuit, which is used to perform
arithmetic functions like addition, subtraction,
multiplication, division etc. is called arithmetic
circuit.
• Typically, an addition operation takes less than 1
µs.
• The logic functions that are commonly used are
EX-OR, OR and AND.
Adder
• In electronics an adder is digital circuit that perform
addition of numbers.
• In modern computer adder reside in the arithmetic
logic unit (ALU).
• Adders are important not only in the computer but
also in many types of digital systems in which the
numeric data are processed.
• There are two basic types of adder:-
– Half Adder & Full Adder
The Half Adder
• The half-adder accepts two binary digits on its inputs and produces two binary digits on its outputs, a sum bit and a carry bit.
Logic Circuits
Simplify to
HOW ???
• Drawback of half adder is, it doesn’t cater to carry i.e. it fails in multi-bit addition.
• It will add A0 and B0, but in next stage we have to add three bits, which will not be done by the circuit, hence we require a FULL ADDER
Exercise
• Using an AND gate and two NOR gates to construct a half adder
The Full Adder
• To overcome the drawback of half adder, full adder is designed.
• It consider Carry also.• The logic circuit which can add 3 bits is
known as Full Adder.• The full adder produces a sum and carry
value, which are both binary digits. • It can be combined with other full
adders.
Full Adder Logic
• A full adder can be constructed from two half adders
by connecting A and B to the input of one half adder,
connecting the sum from that to an input to the
second adder, connecting Ci to the other input and
OR the two carry outputs.
• Equivalently, S could be made the three-bit XOR of
A, B, and Ci, and Co could be made the three-bit
majority function of A, B, and Ci.
The Full-Adder
Exercise
• Write the equation to perform the full adder logic circuits.
Parallel Binary Adder
• Two or more full adders are connected to form parallel binary adders.– To add two binary numbers, a full-adder
is required for each bit in the numbers. – So, for 2-bit numbers, two adders are
needed.
Parallel Binary Adder
• The carry output of each adder is connected to the carry input of the next higher-order adder
Four-Bit Parallel Adders
• A group of 4 bits is called a nibble. A basic 4-bit parallel adder is implemented with four full-adder stages as shown.
Four-Bit Parallel Adders
The carry output of each adder is connected to the carry input of the next higher-order adder as indicated. These are called internal carries.
Parallel Adder Addition
How to performAddition?
Parallel Adder Subtraction
How to performsubtraction?
Testdefination computer
architecture & organization
cache memory
von nuemann
number systemmnemonic, operandflip-flop (jk flip-flop)