# Exercise 8-1: (Problem 8.16) Develop a block diagram and an

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```The German University in Cairo
CSEN 605: Digital System Design
Dr.Mohamed Elmahdy
Eng.Yasmin mohamed
Media Engineering and Technology
Winter 2015
Problem Set 8
ASMD
Discussion: 6/12/2015 – 11/12/2015
The data‐ processing path, commonly referred to as the datapath unit,
manipulates data in registers according to the system’s requirements.
The control unit issues a sequence of commands to the datapath unit. Note
that an internal feedback path from the datapath unit to the control unit
provides status conditions that the control unit uses together with the external
(primary) inputs to determine the sequence of control signals (outputs of the
control unit) that direct the operation of the datapath unit .
Exercise 8-1: (Problem 8.16)
Develop a block diagram and an ASMD chart for a digital circuit that multiplies two binary numbers
by the repeated-addition method. For example, to multiply 5 X 4, the digital system evaluates the
product by adding the multiplicand four times: 5 + 5 + 5 + 5 = 20.
Design the circuit. Let the multiplicand be in register BR, the multiplier in register AR, and the
product in register PR. A zero-detection signal indicates whether AR is 0.
Solution :
• RTL notation:
• s0: (initial state)
• If start = 0 go back to state s0, If (start = 1)
• then BR &lt;= multiplicand,
• AR &lt;= multiplier,
• PR &lt;= 0, go to s1.
• s1: (check AR for Zero
• If Zero = 1 AR = 0, ithen go back to s0 (done)
If (Zero = 0) then go to s1, PR &lt;= PR + BR, AR &lt;= AR – 1.
The internal architecture of the datapath consists of a double-width register to hold the product (PR), a
register to hold the multiplier (AR), a register to hold the multiplicand (BR), a double-width parallel
adder, and single-width parallel adder. The single-width adder is used to implement the operation of
decrementing the multiplier unit. Adding a word consisting entirely of 1s to the multiplier accomplishes
the 2's complement subtraction of 1 from the multiplier.
Page 1
The German University in Cairo
CSEN 605: Digital System Design
Dr.Mohamed Elmahdy
Eng.Yasmin mohamed
Media Engineering and Technology
Winter 2015
Page 2
The German University in Cairo
CSEN 605: Digital System Design
Dr.Mohamed Elmahdy
Eng.Yasmin mohamed
Media Engineering and Technology
Winter 2015
Exercise 8-3: (Problem 8.22)
The figure below shows an alternative ASMD chart for a sequential binary multiplier. Write and verify an
RTL model of the system
Page 3
The German University in Cairo
CSEN 605: Digital System Design
Dr.Mohamed Elmahdy
Eng.Yasmin mohamed
Media Engineering and Technology
Winter 2015
Page 4
The German University in Cairo
CSEN 605: Digital System Design
Dr.Mohamed Elmahdy
Eng.Yasmin mohamed
Media Engineering and Technology
Winter 2015
Page 5
The German University in Cairo
CSEN 605: Digital System Design
Dr.Mohamed Elmahdy
Eng.Yasmin mohamed
Media Engineering and Technology
Winter 2015
Page 6
The German University in Cairo
CSEN 605: Digital System Design
Dr.Mohamed Elmahdy
Eng.Yasmin mohamed
Media Engineering and Technology
Winter 2015
*Exercise 8-4: (Problem 8.29)
An ASMD chart for a finite state machine is shown in the figure below. The register operations are not
specified, because we are interested only in designing the control logic.
(a) Draw the equivalent state diagram.
(b) Write and verify an HDL description of the controller.
Page 7
The German University in Cairo
CSEN 605: Digital System Design
Dr.Mohamed Elmahdy
Eng.Yasmin mohamed
Media Engineering and Technology
Winter 2015
Solution:
Page 8
The German University in Cairo
CSEN 605: Digital System Design
Dr.Mohamed Elmahdy
Eng.Yasmin mohamed
Media Engineering and Technology
Winter 2015
Exercise 8-4 (Problem 8.8 )
Design a digital circuit with three 16‐bit registers AR, BR, and CR that perform the following
operations:
(a) Transfer two 16‐bit signed numbers (in 2’s‐complement representation) to AR and BR .
(b) If the number in AR is negative, divide the number in AR by 2 and transfer the result to
register CR .
(c) If the number in AR is positive but nonzero, multiply the number in BR by 2 and transfer the
result to register CR .
(d) If the number in AR is zero, clear register CR to 0.
(e) Write and verify a behavioral model of the circuit
Page 9
The German University in Cairo
CSEN 605: Digital System Design
Dr.Mohamed Elmahdy
Eng.Yasmin mohamed
Media Engineering and Technology
Winter 2015
Solution :
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The German University in Cairo
CSEN 605: Digital System Design
Dr.Mohamed Elmahdy
Eng.Yasmin mohamed
Media Engineering and Technology
Winter 2015
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The German University in Cairo
CSEN 605: Digital System Design
Dr.Mohamed Elmahdy
Eng.Yasmin mohamed
Media Engineering and Technology
Winter 2015
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