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table.alulogic { border-collapse: collapse; margin: 5px; } table.alulogic th, table.alulogic tr, table.alulogic td { border: 1px solid gray; padding: 5px; text-align: center; } The arithmetic-logic unit is a fundamental part of any computer, performing addition, subtraction, and logic operations, but how it works is a mystery to many people. I've reverse-engineered the ALU circuit from the 8085 microprocessor and explain how it works. The 8085's ALU is a surprisingly complex circuit that at first looks like a mysterious jumble of gates, but it can be understood if you don't mind diving into some Boolean logic. The following diagram shows the location of the ALU in the 8085. The ALU is 8 bits wide, with the high-order bit on the left. The register file is the large block below the ALU. The registers are 16 bits wide, made up of pairs of 8-bit registers. Surprisingly, the register file has the high-order bit on the right, the opposite order from the ALU. [Image] The ALU takes two 8-bit inputs, which I'll call A and X, and performs one of five basic operations: ADD, OR, XOR, AND, and SHIFT-RIGHT. As well, if the input X is inverted, the ALU can perform subtraction and complement operations. You might think SHIFT-LEFT is missing from this list. However, it is simply performed by adding the number to itself, which shifts it to the left one bit in binary. Note that the 8085 arithmetic operations are very basic. There is no multiplication or division operation - these were added in the 8086. The ALU consists of 8 mostly-identical slices, one for each bit. For addition, each slice of the ALU adds the appropriate input bits, computing the sum A + X + carry-in, generating a sum bit and a carry-out bit. That is, each bit of the ALU implements a full adder. The logic operations simply operate on the two input bits: A AND X, A OR X, A XOR X. Shift-right simply outputs the A bit from the slice to the right. ALU schematic The following schematic shows one bit of the ALU. The schematic has roughly the same layout as the implementation on the chip, flowing from bottom to top. Eight of these circuits are stacked side-by-side, with the low-order bit on the right. Carries flow from right to left, and bits shifted right flow from left to right. [Image] Negation Starting at the bottom of the schematic, is the complex gate labeled Negation. This gate optionally selects a negated second argument by selecting either XN or /XN. (XN is the Nth bit of the second argument, which I'll call X. The / indicates the complement.) For most of the discussion below I'll assume XN is uncomplemented to keep things simpler. Operation Above the complement selector are a few gates labeled Operation that perform the desired 2-input operation. The NAND gate on the left generates either A NAND X or 1 based on the select_op1 control line. The OR gate on the right generates either A OR X or 1, based on the select_op2 control line. Combining these in the NAND gate yields four different possibilities: select_op1select_op2Result 00A NOR X 010 10A NXOR X 11A AND X Note that instead of OR and XOR, the complemented value is produced by this circuit. This will be fixed in the next step. Combine with carry Above the operation circuit is the next block of gates labeled Combine with carry that generates the ALU output by merging the carry-in with the operation value via XOR. To understand this circuit, first consider the following simple XOR circuit, which is used a couple times in the ALU. It can be understood fairly simply: if both inputs are 0 (top) or both inputs are 1 (bottom) then the output is 0. [Image] Ignoring the shift_right circuit for a moment, the block of gates is simply the XOR circuit above. Note that XOR with 0 is a no-op, while XOR with 1 complements the value. And A XOR X XOR CARRY is the low-order bit of adding A, X, and CARRY. The key point of this circuit is that the incoming carry is generated with the proper value to convert the operation output into the desired final result. The incoming carry /carry(N-1) is either 0, 1, or the complemented carry from bit N-1 as appropriate. OpOperation outputCarryResult orA NOR X1A OR X addA NXOR X/carryA XOR X XOR CARRY xorA NXOR X1A XOR X andA AND X0A AND X shift right00A(N+1) complementA NOR /X1A OR /X subtractA NXOR /X/carryA XOR /X XOR CARRY Note that the carry-in line must have the right value in order to generate the appropriate output. For addition it passes the inverted carry from one bit to the next. But for OR, XOR, the line is set to 1. And for AND and SHIFT_RIGHT it is set to 0. As will be seen below, the carry circuitry generates the right value for the right operation. The final aspect of this circuit is the shift-right circuit. With a 0 op input, 0 carry input, and shift_right set, the output is simply the bit from the right: A(N+1). Generate carry The circuit on the left, labeled Generate carry generates the carry out. It can generate three different outputs: 1, 0, or the (complemented) carry from the sum. If select_op2 is set, it will force the carry to 0. Otherwise if force_ncarry_1 is set, it will force the carry to 1. Otherwise, the carry is generated for the sum of A + X + carry-in through straightforward logic: If the carry-in is set, and one of the inputs is set, there will be a carry out. If both input bits are set, there will be a carry out. Flags The 8085 has a parity flag, which is 1 if the number of 1 bits is even, and 0 if the number of parity bits is odd. The parity flag is generated by XORing all the result bits together (and complementing). Each bit is XORed with the lower-order parity value by the parity circuit near the top of the schematic. The XOR circuit is the same circuit described above. The zero flag is computed by a simple circuit: each result bit drives a transistor that will pull the zero line low if the bit is set. This forms an 8-input NOR gate, spread across the ALU. The control lines As seen in the schematic, the 8085 uses multiple control lines to control the activity inside the ALU. In total, the ALU provides 7 different operations and the following table summarizes the control lines that are used for each operation. It also lists the opcodes that use each ALU operation. Operationselect_negselect_op1select_op2shift_rightforce_ncarry_1Opcodes or00001ORA,ORI (and default) add01000INR,DCR,RLC,DAD,RAL,DAA,ADD,ADC,ADI,ACI (and undocumented LDSI,LDHI,RDEL) xor01001XRA,XRI and01101ANA,ANI shift right00111RRC,RAR (ARHL) complement10001CMA subtract11000SUB,SBB,SUI,SBI,CMP,CPI (DSUB) The ALU control lines are generated from the opcode by the programmable logic array. Specifically, they are outputs from PLA F, which is to the right of the ALU. More details are in my article on the PLA. The ALU has additional control lines to set up the registers, initialize the carry bits, and set the flags. These control the differences between different op codes, beyond the categories above. the I will explain those in a future article. [Image] Reverse-engineering the ALU This information is based on the 8085 reverse-engineering done by the visual 6502 team. This team dissolves chips in acid to remove the packaging and then takes many close-up photographs of the die inside. Pavel Zima converted these photographs into mask layer images, generated a transistor net from the layers, and wrote a transistor-level 8085 simulator. I took the transistor net and used it to figure out how the ALU works. First, I converted the transistor net into gates. Next I figured out which gates are part of the ALU and put them into a schematic. Then I examined how the circuit worked for different operations and eventually figured out how it works. Conclusion The ALU of the 8085 is an interesting circuit. At first it seemed like an incomprehensible pile of gates with mysterious control lines, but after some investigation I figured it out. The 8085 ALU is implemented very differently from the 6502's ALU (which I'll write up later). The 6502's ALU uses fairly straightforward circuits to generate the SUM, AND, XOR, OR, and SHIFT values in parallel, and then uses a simple pass-transistor multiplexor to pick the desired operation. This is in contrast to the 8085 ALU, which generates only the desired value.