LALU: Lookup Arithmetic Logic Unit

MTM Scientific, Inc

1 MB ROM for Arithmetic Logic Unit

Figure 1: 8 MB EPROM with 20 Address Lines for use as LALU

This page describes the design and development of LALU: Lookup Arithmetic Logic Unit. The LALU functions as the ALU for a simple digital computer design in development. Traditionally an ALU is included in the Central Processing Unit (CPU) of a computer. Stand alone ALUs are also available, such as the venerable 74LS181. This page describes using an 8 MB EPROM (M27C801: Organized as 1MB x 8 Bits) to perform ALU functions on two 8-bit input registers "A" and "B". The 8-bit output appears on IC pins Q7-Q0, which is then registered back into A.

Here are the assignments for the Accumulator "A", B Register "B" and Output.

B Register Inputs: A7, A6, A5, A4, A3, A2, A1, A0 (LSB)
A Register Inputs: A15, A14, A13, A12, A11, A10, A9, A8 (LSB)
ALU Output: Q7, Q6, Q5, Q4, Q3, Q2, Q1, Q0 (LSB)
LALU Function Select Inputs:  A19, A18, A17, A16 (LSB)

The function to be performed by the LALU is chosen by using a 4 bit wide control nibble. A surprising variety of functions can be performed with this simple architecture. Here is our initial assignment for 16 functions for LALU.

Control        Name          Description (Result always sent to A)
0000           AND           Logical AND of A and B
0001            OR              Logical OR of A and B
0010            NOT           Logical NOT of A
0011            INC            Increment A by 1
0100            DEC           Decrement A by 1
0101            RLS            Right Logical Shift
0110            ADD           Addition (A+B)
0111            SUB            Subtraction (A-B)
1000            A>B            Set Flag If A>B
1001            A=B            Set Flag if A=B
1010            A<B            Set Flag if A<B
1011            MBA            Move B to A
1100            MUL            Multiply (A*B)
1101            LAZ            Load A with Zero

The LALU output is always sent to Register A (The starting contents of Register A are subsequently lost.) The contents of Register B are preserved. The flag functions set a binary True/False output (1 or 0) which is sent to Register A. Overflows for addition, subtraction and multiplication are indicated by sending "FF" to A. (Errors must be checked programatically.)

The list of functions chosen here for the LALU is basic. LALU functions could include trigonometric quantities (sine, cosine, etc), coefficients for calculations (FFT, infinite series, etc), other logical functions (NAND, XOR, etc) as well as other flags, bit shifts, rotates and support for complement math. (Presently we use unsigned integer math.)

Here is a link to the HEX file we have defined above. This file is suitable for burning into an EPROM such as the M27C801:  LALU.HEX

The HEX file for burning the EPROM is created using an Excel spreadsheet and hex file editor. The Excel spreedsheet has 1,048,576 rows... corresponding to the 1,048,576 memory locations in the EPROM. Coincidentally, this was the largest number of rows possible in a Microsoft Excel 2007 spreadsheet. The actual HEX file data appears in column D. The table is generated by using conditional logic formulas in the cells of column C. The A and B columns are inputs to the calculation. (Representing registers A and B) The large size of the spreadsheet file makes it difficult to navigate. Hyperlink shortcuts were added to facilitate navigation (See the hot links on the far righthand side of the worksheet).

Excel Spreadsheet for Composing the LALU

Figure 2: Excel Hex File composer for the LALU

A shortcoming of this LALU implementation is the 8-bit nature of register inputs A and B, as well as the output result. A desirable feature for the LALU would be operation as a bit-slice component.  For example, in the case of addition this would require routing an overflow signal to the next LALU bit slice. Unfortunately, this would require dedicating a control line address for the purpose. Consequently, the 4 address lines would be reduced to 3, and instead of 16 functions the LALU would have 8.  Larger programmable ROM's are available, although they present challenges in terms of cost, programming hardware and hex file creation.

Another real world shortcoming of the LALU is the speed of calcuation. The M27C801 chosen here has an access time of 45ns. Many EPROMs have slower access times.  Another shortcoming is that a single-cell entry mistake in the 1 million plus Excel spreadsheet would be difficult to detect in practice. 

Here are some interesting links to similar projects and discourse:

Here is an article about using ROM's for combinational logic.

Here is a fantastic article from Garth Wilson on using ROM's for lookup tables.

Bitwise operations are not native to Excel 2007. Here is a description of how to add them using Visual Basic.