- Review Integer Multiplication
- Examine the Hardware Implementation Procedure
- Review the 4-bit Adder device and use it in multiplier circuits
- Review the 4-bit shifft register device and use it in multiplier circuits
- Build a 4-bit multiplier circuit and test it

The ALU is an important part of any computer. Building an integer multiplier will give us insight of how machines could multiply numbers and it will introduce us to some of the issues of control unit operation.

- Pencil and Paper Approach

Here is an example that requires a 2n-bit adder. 1 0 1 1 Multiplicand (11) x 1 1 0 1 Multiplier (13) ---------------- 1 0 1 1 0 0 0 0 1 0 1 1 Partial Products + 1 0 1 1 ---------------- 1 0 0 0 1 1 1 1 Product (143)

Algorithm of (M x Q): 1. Initilization: A (n-bit) = 0; C (1-bit) = 0; Counter = n; 2. Repeat the following steps until Counter = 0: a) If Q0 (LSB of Q) = 1, then C A = A + M, and Shift C, A, and Q one bit to the right simultaneously. b) If Q0 (LSB of Q) = 0, then shift C, A, and Q one bit to the right simultaneously. c) Counter = Counter - 1. 3. Halt. The product is in A and Q.

Basic Components: a) Register M (n-bit): Stores multiplicand. b) Register Q (n-bit): Stores multiplier. c) Register A (n-bit): Initialized to zero to store the partial product. d) n-bit Adder: Performs addition when Q0 (LSB of Q) is one. e) Register C (1-bit): Holds the end carry of the adder. C, A, Q can be shifted to right simultaneously. f) Control Logic: includes number of iterations and addition and shift operation.

Build the following circuit. Obtain the "Adder-4" from the Simulation Logic library.

It demonstrates the following: 1. How to use the Hex display and Keyboard. 2. How to use the 4 bit adder put hex keyboards on the inputs, a binary probe on the CO (carry out) line, a binary switch on the CI (carry in) line, and a hex display on the output.

Build the following circuit. Obtain the "Shift Reg-4" from the Simulation Logic library.

It demonstrates the following: 1. How to use the 4 bit shift register. 2. How to use the Load and Shift modes. 3. How to use individual probes on each output to make it easier to see what's happening in shift mode. 4. Shifting direction is SI -> Q0 -> Q1 -> Q2 -> Q3. With LD set to 1: The register is in shift mode. The SI (shift input) line is used to set the value to be shifted into the register. Clocking is positive edge triggered. With LD set to 0: The register is in parallel load mode. Inputs D0 to D3 become outputs Q0 to Q3 on the next rising clock pulse.

For the multiplier circuit: You do not build a control unit. You will be the brains of the circuit. The algorithm to use the circuit will be something like:Load up the Q register with the multiplier: LD of Q<- 0 set Hex keypad toggle the Q clock Clear the A register: LD of A<- 1 toggle the clock until clear Repeat 4 times: --------------- IF (LSB of Q = 1) { ADD M register to A register: toggle the C clock LD of A<- 0 toggle the A clock Shift C__A__Q: LD of Q <- 1 toggle the Q clock LD of A <- 1 toggle the A clock } ELSE (LSB of Q = 0) { Shift C__A__Q : LD of Q <- 1 toggle the Q clock LD of A <- 1 toggle the A clock }