ECE 434 Advanced Digital System L13 Electrical and Computer Engineering University of Western Ontario

Review: Block Diagram of a Binary Multiplier Ad – add signal // adder outputs are stored into the ACC Sh – shift signal // shift all 9 bits to right Ld – load signal // load multiplier into the 4 lower bits of the ACC and clear the upper 5 bits 15/11/2018

Review: State Graph for Binary Multiplier 15/11/2018

Review: Multiplier Control with Counter (cont’d) Increment counter each time a shift signal is generated Generate K after n-1 shifts occured 15/11/2018

Review: Array Multiplier What do we need to realize Array Multiplier? AND gates = ? FA = ? HA = ? 15/11/2018

Review: Array Multiplier (cont’d) 15/11/2018

Review: Multiplication of Signed Binary Numbers How to multiply signed binary numbers? Procedure Complement the multiplier if negative Complement the multiplicand if negative Multiply two positive binary numbers Complement the product if it should be negative Simple but requires more hardware and time than other available methods 15/11/2018

Review: Multiplication of Signed Binary Numbers Four cases Multiplicand is positive, multiplier is positive Multiplicand is negative, multiplier is positive Multiplicand is positive, multiplier is negative Multiplier is negative, multiplicand is negative Examples 0111 x 0101 = ? 1101 x 0101 = ? 0101 x 1101 = ? 1011 x 1101 = ? Preserve the sign of the partial product at each step If multiplier is negative, complement the multiplicand before adding it in at the last step 15/11/2018

Review: 2’s Complement Multiplier 15/11/2018

State Graph for 2’s Complement Multiplier 15/11/2018

Faster Multiplier Move wires from the adder outputs one position to the right => add and shift can occur at the same clock cycle 15/11/2018

State Graph for Faster Multiplier 15/11/2018

Behavioral Model for Faster Multiplier 15/11/2018

Behavioral Model for Faster Multiplier 15/11/2018

Command File and Simulation 15/11/2018

Test Bench for Signed Multiplier 15/11/2018

Digital design with SM Charts State graphs used to describe state machines controlling a digital system Alternative: use state machine flowchart 15/11/2018

State Machine Charts SM chart or ASM (Algorithmic State Machine) chart Easier to understand the operation of digital system by examining of the SM chart instead of equivalent state graph SM chart leads directly to hardware realization 15/11/2018

Components of SM charts 15/11/2018

SM chart is constructed from SM blocks State S1 is entered => Z1 and Z2 become 1 if X1=0 Z3 and Z4 become 1 if X1=1 and X3=0 Z5 become 1 15/11/2018

Equivalent SM Blocks 15/11/2018

Equivalent SM Charts for Comb Networks 15/11/2018

Block with Feedback 15/11/2018

Equivalent SM Blocks 15/11/2018

Converting a State Graph to an SM Chart 15/11/2018

Derivation of SM Charts Binary Multiplier Dice Game 15/11/2018

SM Chart for Binary Multiplier 15/11/2018

VHDL for Multiplier SM Chart (I) 15/11/2018

VHDL for Multiplier SM Chart (II) 15/11/2018

Electronic Dice Game Block diagram 1. Two counters simulate the roll of dice (1-6); sum of two counters is in range of 2-12 2. Reset – initiate new game 3. Rb – roll button; when the roll button is pressed the counters count at high speed; when the button is released, the values of counters are displayed and game can proceed. 15/11/2018

Electronic Dice Game - Description First roll player wins if the sum is 7 or 11 player loses if the sum is 2, 3 or 12 otherwise, the sum obtained in the first roll is referred as a point, and player must roll the dice again Second roll (or subsequent roll) player wins if the sum equals the point player loses if the sum is 7 otherwise, player rolls again until she/he finally wins or loses 15/11/2018

Flowchart for Dice Game 15/11/2018

Control Network for Dice Game Input signals to the control network D7 – 1 if the sum of the dice is 1 D711 – (7 or 11) D2312 – (2, 3, 12) Eq – 1 if the sum equals the number stored in the point register Rb – 1 when the roll button is pressed Reset – 1 when the reset button is pressed Output from the control network Roll=1 – enables the dice counters Sp=1 – sum is stored in the point register Win=1 – turns on win light Lose=1 – turns on lose light 15/11/2018

SM Chart for Dice Game 15/11/2018

State Graph for Dice Game 15/11/2018

Behavioral Model for Dice Game (1) 15/11/2018

Behavioral Model for Dice Game (2) 15/11/2018

To Do Read chapters 4.1, 4.2, 4.3 Do homework #4 15/11/2018