Forward Design by state transition table, and state graph

Characteristic table for 4 types of flip-flops

Excitation table for 4 types of flip-flops

Example 1: a sequential machine to detect a sequence of 1011 Design a sequential machine to detect a sequence of 1011. Using first a S-R flip flop, and then Toggle (T ) flip-flop.

1011 sequence detector

Design by state graph: Using a 4-bit multiplier as an example Using 4-bit multiplier as an example, 1101 X 1011 = ? 1101 X 1011 ------------------------------- where 1101: Multiplicand 1011: Multiplier

4-bit parallel multiplier: using one 4-bit adder, and one register with right shift function

The location of the bits in the register at each clock time The location of the bits in the register at each clock time. Using 1011 X 1101 as an example.

State Graph: Counter-based N-bit Multiplier

Counter-based 4-bit multiplier Using 1011 X 1101 as an example

Solution: page 1, using two D Flip-flops

Solution: page 2

Solution: page 3

From State Graph to SM chart design, using 1011 X 1101 as an example

State Graph: Counter-based N-bit Multiplier

State Graph: Counter-based N-bit Multiplier

4-bit Binary Multiplier Design by SM chart (State machine: SM) State graph SM chart

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