Recitation Session 6
CSE341 Computer Organization
University at Buffalo
radhakri@buffalo.edu
March 11, 2016
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Recitation Session Outline
1
Overview of Digital Logic and Design
2
Gates, Truth Tables and Logic Equations
3
Combinational and Sequential Logic
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Introduction to Digital Logic
1
Digital electronics operate with only two voltage levels of
interest - a high and a low voltage
2
Different systems use different voltages. Hence logically 1
represents high and 0 represents low voltage
3
Combinational Logic - No memory. The output of a
combinational block depends only on the current input
4
Sequential Logic - Output can depend on both the input and
the value stored in memory, which is called the state of the
logic block
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Truth Tables
1
Combinational logic block contains no memory, it can be
completely specified by defining the values of the outputs for
each possible set of input values
2
Such a description is normally given as a truth table
3
For a logic block with n inputs, there are 2n entries in the
truth table, since there are that many possible combinations
of input values
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Truth Tables
Consider a logic function with three inputs, A, B, and C, and three
outputs, D, E, and F. The function is defined as follows
1
D is true if at least one input is true
2
E is true if exactly two inputs are true
3
F is true only if all three inputs are true
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Truth Tables
The truth table will contain 23 = 8 entries
Truth tables can completely describe any combinational logic
function; how ever, they grow in size quickly and may not be easy
to understand. What can we do? - Use Boolean Algebra
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Boolean Algebra
All the variables have the values 0 or 1 and, in typical formulations,
there are three operators - AND, OR & NOT
1
D can be formulated as: D = A + B + C
2
F can be formulated as: F = A.B.C
3
How about E?
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Boolean Algebra
E is true if exactly two inputs are true. Think of it in two parts:
what must be true for E to be true (two of the three inputs must
be true), and what cannot be true (all three cannot be true). Thus
we can write E as
((A.B) + (B.C ) + (A.C )).(A.B.C )
We can also derive E by realizing that E is true only if exactly two
of the inputs are true. Then we can write E as an OR of the three
possible terms that have two true inputs and one false input
(A.B.C̄ ) + (B.C .Ā) + (A.C .B̄)
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Logic Gates
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3-Bit Decoder
Can you build a logic-gate implementation for this decoder?
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Sum of Products Representation
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Sum of Products Representation
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ALU - 1 bit Adder
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ALU - 1 bit Adder
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ALU - 1 bit Adder
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ALU - 32 bit Adder
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FSM - Finite State Machine
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FSM - Finite State Machine
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How to Build a Finite State Machine
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Traffic Lights Example
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Traffic Lights Example
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Traffic Lights Example - State Transition Table
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Traffic Lights Example - State Diagram
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Traffic Lights Example - State Equations
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Synchronous and Asynchronous FSM
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Flip Flops
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