Solved–Lab 8: –ALU– Solution

Description

Submission timestamps will be checked and enforced strictly by the CourseWeb; late submissions will not be accepted. Check the due date of this lab on the CourseWeb. Remember that, per the course syllabus, if you are not marked by your recitation instructor as having attended a recitation, your score will be cut in half.

In this lab, you will build a basic 8-bit arithmetic and logic unit (ALU), one of the major workhorses of any computational processor.

Building a One-bit ALU

Recall the following diagram from class for a one-bit ALU, which can perform AND, OR, addition, subtraction, and set if less than operations as shown below:

	Ainvert			Operation
		Binvert		CarryIn
a	0 M			00
		u
	1	x
				01	Result
				M
				u
b				x
		0 M
			u	10
		1	x
Less				11
				CarryOut

Start a new Logisim project, named it lab08.circ, and build the \1-bit ALU” subcir-cuit as shown above. Make sure you have all sevven inputs (a, b, Ainvert, Binvert, CarryIn, Less, and Operation), and all three outputs (Result, Set, and CarryOut). Note that all inputs and outputs are one bit, except for the Operation which is a two-bit input.

You are permitted to use the built-in Adder component from the Arithmetic Library as a useful abstraction to keep your circuit le simpler. Note that you can also built a one-bit adder from scratch just like in Lab 6.

Chaining together a multi-bit ALU

A one-bit ALU is nice, but it is not very useful for computation by itself. We can chain one together with its likeminded friends to get some real work done! In the picture below, we chain together

Lab 8: ALU

eight one-bit ALUs to form an eight-bit ALU:

Bnegate		Operation
Ainvert
a0	CarryIn
b0	ALU0	Result0
	Less
	CarryOut
a1	CarryIn
b1	ALU1	Result1
0	Less
	CarryOut
		Zero
a2	CarryIn
b2	ALU2	Result2
0	Less
	CarryOut
a7	CarryIn	Result7
b7	ALU7	Set
0	Less	Overflow
	CarryOut

Using your 1-bit ALU subcircuit, build the \8-bit ALU” subcircuit detailed above. Your input will include a four-bit ALUOperation code, (consisting of Ainvert, Bnegate, and a two-bit Operation), as well as two eight-bit operands, A and B. Your outputs will include Zero, Overflow, and an eight-bit Result. Be sure to use splitters to split an combine your input and output values inside this subcircuit, so that you main circuit will stay as simple as possible.

Some things to note:

The Bnegate input serves as both the Binvert signal to all of your 1-bit ALUs and the

CarryIn to the ALU for the least signi cant bit (LSB). This is used so that our ALU can support subtraction, since, in two’s complement, A B = A + (:B + 1).

The Zero output should be true (1) if and only if the value of Result is 0. (That is, the value of all of the Result bits is 0.)

Lab 8: ALU

The Overflow output is derived from (but not equal to) the most signi cant bit (MSB) of the Result; that is, the sign bit. You also need to use the sign bits of the two operands A and B. (See slide 60 of the ALU side deck.)

Recall that the Set output is only used from the adder of the MSB. For simplicity, we will allow all of our one-bit ALUs to generate this signal as shown in the Figure above, but we will not connect this signal anywhere when it is not needed.

The Set output is dependent on the Overflow condition and must be inverted if over ow occurs. (This is not shown in the gure; see slide 61 of the ALU slide deck.)

Only the Set signal from the MSB is tied to the Less input of the LSB, as shown in the Figure above. All other Set signals are wired to a constant 0. (You can nd constants under the \Wiring” library.)

Trying it all together

Finally, create a main circuit which uses your 8-bit ALU subcircuit and simple takes in two eight-bit operands A and B and a four-bit ALUOperation code, and returns an eight-bit Result alongside Zero and Overflow signals. Remember that the ALUOperation consists of Ainvert, Bnegate, and Operation, which are used by di erent parts of your ALU.

Test your circuit with a few sample inputs to make sure everything is working properly. Congrat-ulations! You’ve just built a critical component of any processor!

Submission

Submit the le lab08.circ via CourseWeb before the due date stated on the CourseWeb.

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