CS 14 -- Lab 5

Today, we begin the construction of a 4-bit, unsigned integer multiplication circuit. This multiplier is a clocked circuit, so we will need to set up a counter and a clock, as well as some of the important registers to be used.

Clocks and basic diagrams

At the beginning of lab, I will show you our clock boards, which are easier to use than the clock circuits we've been using. You should design your circuit so that it is easy to attach and detach a clock board, as you will need to share them.

Here are some important features of these clock boards:

• Switches that are easier to handle than our pushbuttons.
• Selection between a manually controlled clock signal and an automatically generated one.
• Simple control of the clear line and the manual clock.

You will be building the third and final version of the multiplier circuit presented in class.

Setting up your counter

As mentioned above, this multiplier is a multi-cycle clocked circuit. We need a counter to keep track of the cycles that have passed. Use a single register chip (heretofore a flip-flop, or 273 chip) to build your counter.

• Remember that the easiest design for the counter is as a ring buffer.
• Note that you will wire D1 (the least significant bit's input) directly to power.
• Also note that the output of each bit should be connected to the input of the next, more significant bit (e.g. Q1 should be connected to D2).
• For a 4-bit multiplier, you will actually need a 5 element counter! The first cycle is going to be used to load the inital values into the registers, then the next four are for the actual multiplication.
• Note that you will have some unused bits in the chip. Be sure to wire their inputs to ground to avoid erratic behavior.
• Finally, the clock board will provide the clear line. All memory elements should share that same clear line.

Implement this counter and be sure that it works correctly.

Setting up the data registers

You will need to set up register chips that will hold the multiplicand and the product/multiplier. Notice that the multiplicand register will never have its value shifted, but the product/multiplier will.

• Install a switch bar (a.k.a. DIP switches) on your board. These are devices that have 8 small switches on them. These will allow you easily to select the values that will be multiplied, with four switches to specify the multiplier and the other to specify the multiplicand.
• Set up a register chip that will store the multiplicand. Notice that you will only need to use 4 of the 8 memory elements, so be sure to wire the unused inputs to ground.
• Connect the first 4 switches on your switch bar to the inputs of the multiplicand register.
• Set up a second register that will store the product/multiplier. Notice that all 8 of its memory elements will be used!
• Here is where you must begin to think more about the details of your design. On the first clock cycle, the upper four bits of the product/multiplier should be set to 0, and the lower four bits should take the values from the last four switches on the switch bar. That is, you should initialize the product to 0, and load the multiplier value. On any later clock cycle, the multiplier's bits should shift downward by 1 bit. Design the part of your circuit that will decide whether or not to shift, and then will achieve that shift at each cycle of the clock. Consult the diagram and use a multiplexer chip (157) to control select appropriate inputs based on whether or not the circuit is on the first cycle or some later cycle. Implement the circuit that will control the inputs to this register.

Finishing the lab

If you have gotten this far, then you should begin to design the actual adding circuitry that will be used at each step. You should also design the multiplexer that will control whether or not the multiplicand is taken as the next input to the adder, or all zeros, based on the lowest bit of the multiplier. Remember that we will have next week's lab time as well!