Chapter 5 Programmable ASIC Logic Cells ApplicationSpecific Integrated

Chapter 5 Programmable ASIC Logic Cells Application-Specific Integrated Circuits Michael John Sebastian Smith Addison Wesley, 1997 EGRE 427 Advanced Digital Design Figures from Application-Specific Integrated Circuits , Michael John Sebastian Smith, Addison Wesley, 1997

ASIC Logic Cells l All FPGAs contain a basic logic cell replicated in a regular array across the chip l There are three different types of basic logic cells: n n n multiplexer based look-up table based programmable array based EGRE 427 Advanced Digital Design Figures from Application-Specific Integrated Circuits , Michael John Sebastian Smith, Addison Wesley, 1997

Actel ACT 1 Multiplexer Based Logic Cell l Logic functions can be built by connecting logic signals to some or all of the Logic Module’s inputs and by connecting the remaining Logic Module inputs to VDD or GND Figure 5. 1 The Actel ACT 1 architecture. (a) Organization of the basic cells. (b) The ACT 1 logic module. (c) An implementation using pass transistors. (d) An example logic macro. EGRE 427 Advanced Digital Design Figures from Application-Specific Integrated Circuits , Michael John Sebastian Smith, Addison Wesley, 1997

Shannon’s Expansion Theorem l We can use Shannon’s expansion theorem to expand a function: F = A · F (A = ‘ 1’) + A' · F (A = ‘ 0’) n Where F(A=‘ 1’) is the function evaluated with A=‘ 1’ and F(A=‘ 0’) is the function evaluated with A=‘ 0’ Example: F = A' · B + A · B · C' + A' · B' · C = A · (B · C') + A' · (B + B' · C) F (A = '1') = B · C' is the cofactor of F with respect to ( wrt ) A or FA l l Eventually we reach the unique canonical form , which uses only minterms (A minterm is a product term that contains all the variables of F—such as A · B' · C) Final result for example above should be: F = A' · B · C + A' · B' · C + A · B · C' + A' · B · C' EGRE 427 Advanced Digital Design Figures from Application-Specific Integrated Circuits , Michael John Sebastian Smith, Addison Wesley, 1997

Using Shannon’s Expansion Theorem to Map a Function to an ACT 1 Logic Module l Another example: F = (A · B) + (B' · C) + D Expand F wrt B: F = B · (A + D) + B' · (C + D) = B · F 2 + B' · F 1 Where F 1= (C + D) and F 2 = (A + D) l The function F can be implemented by 2: 1 MUX, with B selecting between two inputs: F (B = '1') and F (B = '0') n l F also describes the output of the ACT 1 LM Now we need to split up F 1 and F 2 Expand F 1 wrt C: F 1 = C + D = (C · 1) + (C' · D) Expand F 2 wrt A: F 2 = A + D = (A · 1) + (A' · D); l l C connects to the select line of a first-level mux in the ACT 1 LM with ‘ 1’ and D as the inputs to the mux A connects to the select line of another first-level mux in the ACT 1 LM with ‘ 1’ and ‘D’ as inputs to the mux B connects to the select line of the output mux with F 1 and F 2, the outputs of the first level muxes, connected to the inputs See Figure 5. 1(d) for implementation EGRE 427 Advanced Digital Design Figures from Application-Specific Integrated Circuits , Michael John Sebastian Smith, Addison Wesley, 1997

Ways to Arrange a Karnaugh Map of 2 Variables Figure 5. 2 The logic functions of two variables. EGRE 427 Advanced Digital Design Figures from Application-Specific Integrated Circuits , Michael John Sebastian Smith, Addison Wesley, 1997

Boolean Functions of Two Variables Using a 2: 1 Mux EGRE 427 Advanced Digital Design Figures from Application-Specific Integrated Circuits , Michael John Sebastian Smith, Addison Wesley, 1997

ACT 1 LM as a Function Wheel (cont. ) l A 2: 1 MUX is a function wheel that can generate BUF, INV, AND-11, AND 1 -1, OR, AND l Define a function WHEEL (A, B) = MUX (A 0, A 1, SA) l MUX (A 0, A 1, SA) = A 0 · SA' + A 1 · SA l Each of the inputs (A 0, A 1, and SA) may be A, B, '0', or '1' l The ACT 1 LM is built from two function wheels, a 2: 1 MUX, and a two-input OR gate: ACT 1 LM = MUX [WHEEL 1, WHEEL 2, OR (S 0, S 1)] EGRE 427 Advanced Digital Design Figures from Application-Specific Integrated Circuits , Michael John Sebastian Smith, Addison Wesley, 1997

ACT 1 LM as a Function Wheel Figure 5. 3 The ACT 1 logic module as a boolean function generator. (a) A 2: 1 MUX viewed as a logic wheel. (b) The ACT 1 logic module viewed as two function wheels. EGRE 427 Advanced Digital Design Figures from Application-Specific Integrated Circuits , Michael John Sebastian Smith, Addison Wesley, 1997

Example of Implementing a Function with an ACT 1 LM l Example of using the WHEEL functions to implement: F = NAND (A, B) = (A · B)’ 1. First express F as the output of a 2: 1 MUX: expand F wrt A (or wrt B; since F is symmetric) F = A · (B') + A' · ('1') 2. Assign WHEEL 1 to implement INV (B), and WHEEL 2 to implement '1' 3. Set the select input to the MUX connecting WHEEL 1 and WHEEL 2, S 0 + S 1 = A. We can do this using S 0 = A, S 1 = '1' l l A single Actel ACT 1 LM can implement all combinational twoinput functions, most three input functions and many four input functions A transparent D latch can be implemented with one ACT 1 LM and an edge triggered D flip-flop can be implemented with two LM’s EGRE 427 Advanced Digital Design Figures from Application-Specific Integrated Circuits , Michael John Sebastian Smith, Addison Wesley, 1997

Actel ACT 2 and ACT 3 Logic Modules Figure 5. 4 The ACT 2 and ACT 3 logic modules. (a) The C-module. (b) The ACT 2 Smodule. (c) The ACT 3 S-module. (d) The equivalent circuit of the SE. (e) The SE configured as a positive edgetriggered D flip-flop. EGRE 427 Advanced Digital Design Figures from Application-Specific Integrated Circuits , Michael John Sebastian Smith, Addison Wesley, 1997

Actel Timing Model l l Exact delay values in Actel FPGAs can not be determined until interconnect delay is known - i. e. , place and route are done Critical path delay between registers is: t. PD + t. SUD + t. CO There is also a hold time for the flipflops - t. H The combinational logic delay t. PD is dependent on the logic function (which may take more than one LM) and the wiring delays The flip-flop output delay t. CO can also be influenced by the number of gates it drives (fanout) Figure 5. 5 The Actel ACT timing model. (a) The timing parameters for a ‘std’ speed grade ACT 3. (b) Flip-flop timing. (c) An example of flip-flop timing based on ACT 3 parameters. EGRE 427 Advanced Digital Design Figures from Application-Specific Integrated Circuits , Michael John Sebastian Smith, Addison Wesley, 1997

Xilinx Configurable Logic Block (CLB) Figure 5. 6 The Xilinx XC 3000 CLB (configurable logic block). EGRE 427 Advanced Digital Design Figures from Application-Specific Integrated Circuits , Michael John Sebastian Smith, Addison Wesley, 1997

Xilinx CLB (cont. ) l The combinational function in a CLB is implemented with a 32 bit look-up table (LUT) n n l l LUT values are stored in 32 bits of SRAM CLB delay is fixed and equal to the LUT access time There are seven inputs to the LUT, the five CLB inputs (A-E) and the flip-flop outputs (QX and QY) and two outputs (F, G) There are several ways to use the LUT: n n You can use five of the seven possible inputs (A-E<QX, QY) with the entire LUT - the outputs (F, G) are identical You can split the 32 -bit LUT in half to implement two functions of four variables ¦ ¦ n The input variable can be chosen from A-E, QX, QY Two of the inputs must come from A-E You can split the LUT in half and use one of the seven input variables to select between the F and G output - allows some functions of seven variables to be implemented EGRE 427 Advanced Digital Design Figures from Application-Specific Integrated Circuits , Michael John Sebastian Smith, Addison Wesley, 1997

Xilinx XC 4000 Logic Block l l Cell contains 2 four-input LUTs that feed a three input LUT Cell also has special fast carry logic hard-wired between CLBs Figure 5. 7 The Xilinx XC 4000 CLB (configurable logic block). EGRE 427 Advanced Digital Design Figures from Application-Specific Integrated Circuits , Michael John Sebastian Smith, Addison Wesley, 1997

Xilinx XC 5200 Logic Block l l Basic Cell is called a Logic Cell (LC) and is similar to, but simpler than, CLBs in other Xilinx families Term CLB is used here to mean a group of 4 LCs (LC 0 -LC 3) Figure 5. 8 The Xilinx XC 5200 LC (logic cell) and CLB (configurable logic block). EGRE 427 Advanced Digital Design Figures from Application-Specific Integrated Circuits , Michael John Sebastian Smith, Addison Wesley, 1997

Implementing Functions with Xilinx CLBs l Combinational logic functions all have the same delay - a 5 input NAND is as slow (fast) as an inverter l For maximum efficiency, the tools must group logic functions into blocks the utilize the CLB efficiently (i. e. , utilize an high percentage of its functionality) l LUT simplifies the timing model when using synchronous logic l The LUT matches the Xilinx SRAM programming technology well l SRAM within the LUT can be used a general purpose, on-chip SRAM, but it is expensive EGRE 427 Advanced Digital Design Figures from Application-Specific Integrated Circuits , Michael John Sebastian Smith, Addison Wesley, 1997

Xilinx Timing Model Figure 5. 9 The Xilinx LCA timing model. EGRE 427 Advanced Digital Design Figures from Application-Specific Integrated Circuits , Michael John Sebastian Smith, Addison Wesley, 1997

Altera FLEX Architecture l l Basic Cell is called a Logic Element (LE) and resembles the Xilinx XC 5200 LC architecture Altera FLEX uses the same SRAM programming technology as Xilinx Figure 5. 10 The Altera FLEX architecture. (a) Chip floorplan. (b) LAB (Logic Array Block). (c) Details of the LE (logic element). Figures from Application-Specific Integrated Circuits , Michael John Sebastian EGRE 427 Advanced Digital Design Smith, Addison Wesley, 1997

Programmable Logic Array l l Programmable AND array feeding into an OR array can implement a canonical sum-of-products form of an expression n-channel EPROM transistors wired to a pullup resistor can implement a wired-AND function of the inputs n n Output is high only when all the inputs are high The inputs must be inverted Figure 5. 11 Logic Arrays. (a) Two-level logic. (b) Organized sum of products. (c) A programmable. AND plane. (d) EPROM logic array. (e) Wired logic. EGRE 427 Advanced Digital Design Figures from Application-Specific Integrated Circuits , Michael John Sebastian Smith, Addison Wesley, 1997

Registered PAL Figure 5. 12 A registered PAL with I inputs, j product terms, and k macrocells. EGRE 427 Advanced Digital Design Figures from Application-Specific Integrated Circuits , Michael John Sebastian Smith, Addison Wesley, 1997

Logic Expander l l l A logic expander is an output line of the AND array that feeds back as an input to the array itself Logic expanders can help implement functions that require more product terms than are available in a simple PAL Consider implementing this function in in a three-wide OR array: F = A’ · C · D + B’ · C · D + A · B + B · C’ l This can be rewritten as a “sum of (products of products): F = (A’ + B’) · C · D + (A + C’) · B F = (A · B)’ (C · D) + (A’ · C)’ · B l Logic expanders can be used to form the expander terms (A · B)’ and (A’ · C)’ l Logic expanders require an extra pass through the AND array, increasing delay EGRE 427 Advanced Digital Design Figures from Application-Specific Integrated Circuits , Michael John Sebastian Smith, Addison Wesley, 1997

Logic Expander Implementation Figure 5. 13 Expander logic and programmable inversion. EGRE 427 Advanced Digital Design Figures from Application-Specific Integrated Circuits , Michael John Sebastian Smith, Addison Wesley, 1997

Simplifying Logic with Programmed Inversion Figure 5. 14 Use of programmed inversion to simplify logic. (a) The function F = A·B’+ A·C’+ A·D’+ A’·C·D requires four product terms to implement while (b) the complement F’ = A·B·C·D+ A’·D’+ A’·C’ requires only three product terms. EGRE 427 Advanced Digital Design Figures from Application-Specific Integrated Circuits , Michael John Sebastian Smith, Addison Wesley, 1997

Altera MAX Architecture l Macrocell features: n n Wide, programmable AND array Narrow, fixed OR array Logic Expanders Programmable inversion Figure 5. 15 The Altera MAX architecture. (a) Organization of logic and interconnect. (b) A MAX family LAB (Logic Array Block). (c) A MAX family macrocell. EGRE 427 Advanced Digital Design Figures from Application-Specific Integrated Circuits , Michael John Sebastian Smith, Addison Wesley, 1997

Altera MAX Timing Model Figure 5. 16 The timing model for the Altera MAX architecture. (a) A direct path through the logic array and a register. (b) Timing for the direct path. (c) Using a parallel expander. (d) Parallel expander timing. (e) Making two passes through the logic array to use a shared expander. (f) Timing for the shared expander. EGRE 427 Advanced Digital Design Figures from Application-Specific Integrated Circuits , Michael John Sebastian Smith, Addison Wesley, 1997