841 Munch

841 : Munch

Design render

How it works

This generates VGA output for a munching squares animation plus some other stuff, and some simple music. It uses the VGA and audio PMODs listed below.

<img src="munch.png">

Clock generation

A clock generator module divides the main clock clk and vsync into two derived clocks - a 393kHz PWM clock for audio output, and a 10Hz "audio tick" clock that drives the pattern sequencer. The clock generator also provides counters for PWM, volume modulation, and audio pattern sequencing.

LFSR

An 11-bit LFSR provides a noise source. It is an XNOR type, shifting down towards the LSB and inserting the new bit at MSB. XNOR taps are on bits 0 and 2. Bits 0-5 of the LFSR register are used to provide a noise channel and randomized video noise dithering.

Video

The video output is the standard 640x480 @ 60Hz, using a 25.175MHz pixel clock and negative polarity HSYNC/VSYNC. Timing is implemented with a simple two-counter design shamelessly stolen from the Tiny Tapeout VGA playground.

A fixed palette of eight colors is used, and eight brightness levels are created by mixing random bits with the 2-bit per channel brightness levels. Video is output on three layers - the background and layers 0 and 1. A non-black pixel overrides a pixel on any lower layer.

Audio

Audio comes from a basic PSG inspired by the SN76489. There are four channels of sound based on 12-bit timers - three pulse channels and one noise channel. The only real difference between a pulse channel and a noise channel is that the pulse channel flips state when the timer counts down, and the noise channel takes a random state from the LFSR. Each channel also has a two-bit volume level.

The 25.175MHz clock is divided by a 6-bit counter to create a 393KHz PWM output. 6-bits gives 64 possible levels. The PWM high period is a simple sum of the four channels' volumes at any given instant (multiplied by two with the low bit dithered from the LFSR). This does mean the PWM will glitch if volume levels change in the middle of a PWM cycle, but that's fine in practice since it's all low-pass filtered anyway.

The four channels are programmed through a sequencer that provides note and volume data to the PSG. The sequencer is clocked by dividing VSYNC by 6, so the sequencer moves through pattern rows at 10Hz, or 600 ticks per minute. Each pattern of 16 ticks represents one measure, four beats, which means the music proceeds at 150 BPM.

The sequencer cycles through pre-programmed patterns of notes. Note timer data is read from an indirected list of notes, then connected directly to the PSG reload values. This does mean the oscillators are not synchronized at note start. Volumes are modulated through a single repeating pattern per channel, indexed from the top two bits of the sequencer div-by-6 clock divider. This means the volume is a three-step pattern cycling at the start of each pattern tick.

Text Generator

On-screen text uses a segmented approach, where each segment is defined by a mathematical description of a line segment. Each character is then defined by which segments are off or on, like a multi-segment LED display. So text is generated at full resolution despite its large size; each character is 50x100 pixels.

The text generator is just a sequencer over an input bit stream, indexed by the horizonal and vertical position. In this implementation the input is at most six characters long. The text can be positioned arbitrarily, but for this demo it is fixed.

Stage Sequencer

A slower stage clock is derived from the pattern clock. It ticks once every pattern cycle, and drives an overarching "stage sequencer". Each stage counts down for a pre-programmed number of patterns, then switches to the next. The stage number is used in various logic to change the text and colors over time.

Extra outputs

In addition to the audio and video, the three highest bits of the internal pattern counter are output on uio_out[6:4]. The two highest bits count out the four beats in a pattern, and bit 1 has a negative edge at the beginning of each beat. This could be used for beat synchronization with external systems - I just used it for debugging.

How to test

Set the input clock for 25.175MHz. The Pico/RP2040 can output 25.177MHz on GPOUT0 with a 125MHz main clock and a divider of 4 [integer part] and 247 [fractional part]. This worked on my TV.

Reset, and enjoy. :)

External hardware

IO

#InputOutputBidirectional
0R1
1G1
2B1
3VSYNC
4R0beat clock bit 1 (output)
5G0beat clock bit 2 (output)
6B0beat clock bit 3 (output)
7HSYNCaudio (output)

Chip location

Controller Mux Mux Mux Mux Mux Mux Mux Mux Mux Mux Mux Mux Mux Mux Mux Mux Mux Mux Mux Mux Mux Mux Mux Mux Mux Mux Mux Mux tt_um_chip_rom (Chip ROM) tt_um_factory_test (Tiny Tapeout Factory Test) tt_um_tommythorn_maxbw (Asynchronous Multiplier) tt_um_mattvenn_rgb_mixer (RGB Mixer demo5) tt_um_find_the_damn_issue (Find The Damn Issue) tt_um_brandonramos_VGA_Pong_with_NES_Controllers (VGA Pong with NES Controllers) tt_um_kb2ghz_xalu (4-bit minicomputer ALU) tt_um_a1k0n_demo (Demo by a1k0n) tt_um_zec_square1 ("SQUARE-1": VGA/audio demo) tt_um_jmack2201 (Sprite Bouncer with Looping Background Options) tt_um_ran_DanielZhu (Dice) tt_um_gfg_development_tinymandelbrot (TinyMandelbrot) tt_um_toivoh_demo_tt08 (Sequential Shadows [TT08 demo competition]) tt_um_quarren42_demoscene_top (asic design is my passion) tt_um_crispy_vga (Crispy VGA) tt_um_MichaelBell_canon (TT08 Pachelbel's Canon demo) tt_um_shuangyu_top (Calculator) tt_um_wokwi_407306064811090945 (DDR throughput and flop aperature test) tt_um_favoritohjs_scroller (VGA Scroller) tt_um_tt08_wirecube (Wirecube) tt_um_vga_glyph_mode (Glyph Mode) tt_um_a1k0n_vgadonut (VGA donut) tt_um_roy1707018 (RO) tt_um_sign_addsub (CMOS design of 4-bit Signed Adder Subtractor) tt_um_patater_demokit (Patater Demo Kit Waggling Rainbow on a Chip) tt_um_simon_cipher (simon_cipher) tt_um_thexeno_rgbw_controller (RGBW Color Processor) tt_um_demosiine_sda (DemoSiine) tt_um_bytex64_munch (Munch) tt_um_cfib_demo (cfib Demoscene Entry) tt_um_Richard28277 (4-bit ALU) tt_um_betz_morse_keyer (Morse Code Keyer) tt_um_nvious_graphics (nVious Graphics) tt_um_ezchips_calc (8-Bit Calculator) tt_um_hack_cpu (HACK CPU) tt_um_ring_divider (Divided Ring Oscillator) tt_um_ephrenm_tsal (TSAL_TT) tt_um_kapilan_alarm (Alarm Clock) tt_um_stochastic_addmultiply_CL123abc (Stochastic Multiplier, Adder and Self-Multiplier) tt_um_dlfloatmac (DL float MAC) tt_um_faramire_rotary_ring_wrapper (Rotary Encoder WS2812B Control) tt_um_i2c_peripheral_stevej (i2c peripherals: leading zero count and fnv-1a hash) tt_um_yuri_panchul_schoolriscv_cpu_with_fibonacci_program (schoolRISCV CPU with Fibonacci program) tt_um_yuri_panchul_adder_with_flow_control (Adder with Flow Control) tt_um_brailliance (Brailliance) tt_um_nyan (nyan) tt_um_MichaelBell_mandelbrot (VGA Mandelbrot) tt_um_fountaincoder_top_ad (pulse_add) tt_um_edwintorok (Rounding error) tt_um_mac (MAC) tt_um_dpmu (DPMU) tt_um_JAC_EE_segdecode (7 Segment Decode) tt_um_yuri_panchul_sea_battle_vga_game (Sea Battle) tt_um_benpayne_ps2_decoder (PS2 Decoder) tt_um_meriac_play_tune (Super Mario Tune on A Piezo Speaker) tt_um_comm_ic_bhavuk (Comm_IC) tt_um_daosvik_aesinvsbox (AES Inverse S-box) tt_um_cattuto_sr_latch (TT08 - experiments with latch-based shift registers) tt_um_silice (Warp) tt_um_jayjaywong12 (mulmul) tt_um_emmyxu_obstacle_detection (Obstacle Detection) tt_um_neural_navigators (Neural Net ASIC) tt_um_resfuzzy (resfuzzy) tt_um_cejmu (CEJMU Beers and Adders) tt_um_16_mic_beamformer_arghunter (16 Mic Beamformer) tt_um_pdm_pitch_filter_arghunter (PDM Pitch Filter) tt_um_pdm_correlator_arghunter (PDM Correlator) tt_um_ddc_arghunter (DDC) tt_um_i2s_to_pwm_arghunter (I2S to PWM ) tt_um_supermic_arghunter (Supermic ) tt_um_dmtd_arghunter (DMTD ) tt_um_htfab_bouncy_capsule (Bouncy Capsule) tt_um_samuelm_pwm_generator (PWM generator) tt_um_toivoh_demo_deluxe (Sequential Shadows Deluxe [TT08 demo competition]) tt_um_faramire_stopwatch (Simple Stopwatch) tt_um_johshoff_metaballs (Metaballs) tt_um_top (Flame demo) tt_um_NicklausThompson_SkyKing (SkyKing Demo) tt_um_Electom_cla_4bits (4-bit CLA) tt_um_vga_cbtest (Generate VGA output for Color Blindness Test) tt_um_zoom_zoom (Zoom Zoom) tt_um_dpmunit (DPM_Unit) tt_um_clock_divider_arghunter (Clock Divider ) tt_um_dlmiles_poc_fskmodem_hdlctrx (FSK Modem +HDLC +UART (PoC)) tt_um_emilian_muxpga (TinyFPGA resubmit for TT08) tt_um_pyamnihc_dummy_counter (Dummy Counter) tt_um_whynot (Why not?) tt_um_dlmiles_tt08_poc_uart (UART) tt_um_dendraws_donut (donut) tt_um_tmkong_rgb_mixer (RGB Mixer) tt_um_led_matrix_ayla_lin (32x8 LED Matrix Animation) tt_um_rebeccargb_tt09ball_screensaver (TT09Ball VGA Screensaver) tt_um_rebeccargb_vga_pride (VGA Pride) tt_um_levenshtein (Fuzzy Search Engine) tt_um_rebeccargb_colorbars (Color Bars) tt_um_jamesrosssharp_1bitam (1bit_am_sdr) tt_um_rebeccargb_hardware_utf8 (Hardware UTF Encoder/Decoder) tt_um_rebeccargb_styler (Styler) tt_um_rebeccargb_vga_timing_experiments (VGA Timing Experiments) tt_um_rebeccargb_universal_decoder (Universal Binary to Segment Decoder) tt_um_rebeccargb_intercal_alu (INTERCAL ALU) tt_um_toivoh_pio_ram_emu_example (pio-ram-emulator example: Julia fractal) tt_um_tobimckellar_top (Simple PWM Module) tt_um_JesusMinguillon_freqSweep (freqSweep) tt_um_led_cipher (LED Bitserial Cipher) tt_um_my_elevator (Elevator Design) tt_um_wokwi_413387065339458561 (APA102 to WS2812 Translator) tt_um_wokwi_413386991502909441 (SPI Logic Analyzer with Charlieplexed Display) tt_um_alf19185_ALU (4 bit ALU ) tt_um_rtfb_collatz (Collatz conjecture brute-forcer) tt_um_senolgulgonul (Senol Gulgonul tt09) tt_um_Esteban_Oman_Mendoza_maze_2024_top (Space Detective Maze Explorer) tt_um_sebastienparadis_hamming_top (Hamming Code (7,4)) tt_um_prefix8 (tiny-tapeout-8bit-GPTPrefixCircuit) tt_um_lif_tk (LIF on a Ring Topology) tt_um_asheldon44_dsm_decimation_filter (Delta-Sigma ADC Decimation Filter) tt_um_juarez_jimenez (an lfsr with synaptic neurons (excitatory or inhibitatory)) tt_um_lif_clarencechan28 (Perceptron) tt_um_uart_mvm (Matmul System) tt_um_algofoogle_tt09_ring_osc (Verilog ring oscillator) tt_um_pid_controller (PID Controller) tt_um_frequency_counter (Frequency Counter SSD1306 OLED) tt_um_delta_liafn (Delta RNN and Leaky Integrate-and-Fire Nueron Circuit) tt_um_devinatkin_basys3_uart (Basys 3 Over UART Link) tt_um_pwm_top (Generador PWM multiproposito con frecuencia y ciclo de trabajo modulable) tt_um_lfsr_stevej (Linear Feedback Shift Register) tt_um_jamesrosssharp_tiny1bitam (Tiny 1-bit AM Radio) tt_um_instrumented_ring_oscillator (instrumented_ring_oscillator) tt_um_lif1 (STDP Circuit) tt_um_alif (3 Neuron ALIF) tt_um_tiny_ternary_tapeout (T3 (Tiny Ternary Tapeout)) tt_um_snn_with_delays_paolaunisa (ChatGPT-generated Spiking Neural Network with Delays) tt_um_arandomdev_fir_engine_top (FIREngine) tt_um_carryskip_adder8 (8-bit carry-skip) tt_um_riscv_mini (RISC-V Mini) tt_um_CLA8 (8-bit Carry Look-Ahead Adder) tt_um_hybrid_adder (Hybrid_Adder_8bit) tt_um_uart_mvm_sys (Matmul System) tt_um_MichaelBell_hd_8b10b (8b10b decoder and multiplier) tt_um_program_counter_top_level (Test Design 1) tt_um_murmann_group (Decimation Filter for Incremental and Regular Delta-Sigma Modulators) tt_um_adder_accumulator_sathworld (adder-accumulator) tt_um_control_block (ECE 298A 8-Bit CPU Control Block) tt_um_LFSR_Encrypt (LFSR Encrypter) tt_um_cdc_test (SkyKing Demo) tt_um_two_lif_stdp (Two LIF Neurons with STDP Learning) tt_um_underserved (ITS-RISCV) tt_um_znah_vga_ca (znah_vga_ca) tt_um_mikegoelzer_7segmentbyte (7-Segment Byte Display) tt_um_idann (Forward Pass Network for Simple ANN) tt_um_carryskip_adder9 (carry skip adder) tt_um_mroblesh (Frequency Encoder and Decoder) tt_um_wokwi_411379488132926465 (Semana UCU Verilog) tt_um_rejunity_atari2600 (Atari 2600) tt_um_rejunity_z80 (Zilog Z80) tt_um_couchand_cora16 (CORA-16) tt_um_kashmaster_carryskip (8-bit-CARRY_SKIP) tt_um_tiny_ternary_tapeout_csa (T3 (Tiny Ternary Tapeout) CSA ) tt_um_array_secD7 (Tiny Tapeout Group 7 Lab D) tt_um_chip4lyfe (Leaky Integrate Fire Neuron) tt_um_ronikant_jeremykam_tinyregisters (Tiny Registers) tt_um_VanceWiberg_top (Team 17's 8 bit DAC) tt_um_claudiotalarico_counter (4-bit up/down binary counter) tt_um_gmejiamtz (Configurable Logic Block) tt_um_I2C (I2C and SPI) tt_um_perceptron_mtchun (Perceptron Neuron) tt_um_histogramming (Histogramming) tt_um_gfcwfzkm_scope_bfh_mht1_3 (Basic Oszilloscope and Signal Generator) tt_um_MichaelBell_rle_vga (RLE Video Player) tt_um_ece298a_8_bit_cpu_top (8-Bit CPU) tt_um_Coline3003_top (15 channels emission counter) tt_um_dlmiles_dffram32x8_2r1w (Tiny RAM DFF 2r1w) tt_um_urish_sic1 (SIC-1 8-bit SUBLEQ Single Instruction Computer) tt_um_Coline3003_spect_top (Spectrogram extractor, 2 channels) tt_um_CarrySelect8bit (carry_select) tt_um_koggestone_adder8 (test_friday2) tt_um_Rapoport (Perceptron) tt_um_cellular_alchemist (Hopfield Network with Izhikevich-type RS and FS Neurons) tt_um_tinysynth (Tinysynth) tt_um_wokwi_414120248222232577 (A Tale of Two NCOs) tt_um_a1k0n_nyancat (VGA Nyan Cat) tt_um_tommythorn_workshop (Workshop demo) tt_um_lrc_stevej (LRC - Longitudinal Redundancy Check generator) tt_um_shifter (Shifter) tt_um_schoeberl_test (tinydsp-lol) tt_um_anislam (Leaky integrate and fire spiking neural network) tt_um_systolicLif (Basic model for Systollic array implementation of LIF) tt_um_algofoogle_tt09_ring_osc2 (Verilog ring oscillator V2) tt_um_dff_mem (dff_mem) tt_um_nomuwill (16 Bit Izhikevich Neuron) tt_um_digital_clock_example (7-Segment Digital Desk Clock) tt_um_udxs (Basic Perceptron + ReLU) tt_um_matrix_mult (Basic Matrix-Vector Multiplication) tt_um_db_MAC (8 bit MAC Unit) tt_um_anas_7193 (Programmable PWM Generator) tt_um_flyingfish800 (Verilog test project) tt_um_project_tt09 (Basic LIF Neuron) tt_um_lifn (Integrate-and-Fire Neuron Circuit) tt_um_rejunity_e2m0_x_i8_matmul (E2M0 x INT8 Systolic Array) tt_um_michaelmcculloch_alu (Michaels Tiny Tapeout ALU) tt_um_dog_BILBO (8-bit CBILBO) tt_um_stochastic_integrator_tt9_CL123abc (Stochastic Integrator) tt_um_samkho_two_channel_square_wave_generator (TwoChannelSquareWaveGenerator) tt_um_urish_giant_ringosc (Giant Ring Oscillator (3853 inverters)) tt_um_htfab_caterpillar (Simon's Caterpillar) tt_um_purdue_socet_uart (SoCET UART with FIFO buffers) tt_um_rejunity_sn76489 (Classic 8-bit era Programmable Sound Generator SN76489) tt_um_rejunity_ay8913 (Classic 8-bit era Programmable Sound Generator AY-3-8913) tt_um_tommythorn_cgates (Cgates) tt_um_09eksdee (eksdee) tt_um_rejunity_decoder (ternary, E1M0, E2M0 decoders) tt_um_kailinsley (Dynamic Threshold Leaky Integrate-and-Fire) tt_um_rejunity_vga_test01 (VGA Drop (audio/visual demo)) tt_um_wallento_4bit_toycpu (4-Bit Toy CPU) tt_um_warp (Warp) tt_um_algofoogle_tt09_ring_osc3 (Verilog ring oscillator V3) tt_um_kev_ma_matmult222 (2-bit 2x2 Matrix Multiplier) tt_um_rejunity_vga_logo (VGA Tiny Logo (1 tile)) tt_um_liaf (A simple leaky integrate and fire neuron) tt_um_lif_network_MR (Leaky Neuron Network) tt_um_lsnn_hschweig (Neuromorphic Hardware for SNN LSTM) tt_um_Nishanth_RISCV (RISCV Processor Design) tt_um_KoushikCSN_RISCV (RISCV Processor Design) tt_um_ccu_goatgate (tiny cipher 4 bit key) tt_um_lif_ZB (Tutorial: Simple LIF Neuron) tt_um_z2a_rgb_mixer (RGB Mixer demo) tt_um_vga_clock (VGA clock) tt_um_synth_simple_mm (synth_simple) tt_um_gus16 (GUS16 CPU) tt_um_rejunity_ternary_dot (Ternary 128-element Dot Product) tt_um_virantha_enigma (Enigma - 52-bit Key Length) tt_um_atomNPU (AtomNPU) tt_um_alphaonesoc (AlphaOneSoC) tt_um_gxrii_spi_sevenseg (SPI 7-segment display) tt_um_urish_simon (Simon Says memory game) tt_um_branch_pred (TinyTapeout Minimal Branch Predictor) tt_um_xor_encryption (Xor-Logic) tt_um_MAC_Accelerator_OnSachinSharma (MAC Operation) tt_um_moody_mimosa (Moody-mimosa) tt_um_wrapper (6Digit7SegClock) tt_um_MichaelBell_tinyQV (TinyQV Risc-V SoC) tt_um_devmonk_ay8913 (Classic 8-bit era Programmable Sound Generator AY-3-8913) tt_um_toivoh_demo_tt10 (Orion Iron Ion [TT08 demo competition]) tt_um_2048_vga_game (2048 sliding tile puzzle game (VGA)) tt_um_gamepad_pmod_demo (Gamepad Pmod Demo) tt_um_tinytapeout_logo_screensaver (VGA Screensaver with Tiny Tapeout Logo) tt_um_mattvenn_spi_test (SPI test) tt_um_huffman_coder (Huffmann_Coder) tt_um_multiplier_tt10 (Vedic multiplier) tt_um_schoeberl_wildcat (Wildcat RISC-V) tt_um_kentrane_tinyspectrum (Tiny piano) tt_um_i2c_regf (Asynchronous I2C Registerfile Interface) tt_um_tappu_tobias1012 (Tappu) tt_um_mp_lif_schor (mp_LIF_neuron) tt_um_asgerwenneb (Custom SRAM) tt_um_Strider93 (digital LIF Neuron) tt_um_wokwi_422960078645704705 (Hero on Tape) tt_um_keszocze_ssmcl (SSMCl) tt_um_luke_clock (TT10_Luke_Clock) tt_um_enjens (Verilog based clock to 7-segment counter) tt_um_UartMain (XOR Cipher) tt_um_torurstrom_async_lock (Asynchronous Locking Unit) tt_um_larva (LaRVa CPU) tt_um_zhouzhouthezhou_adder (tt10_zhouzhouthezhou_adder) tt_um_jp_cd101_saw (KCH CD101 Saw Synth) tt_um_hpdl1414_uart_atudoroi (TT10 HPDL 1414 Uart) tt_um_jun1okamura_test0 (7-segment with LFSR) tt_um_strau0106_simple_viii (simple-viii) tt_um_obriensp_jtag (JTAG TAP) tt_um_10_vga_crossyroad (Crossyroad) tt_um_bilal_trng (TRNG) tt_um_space_invaders_game (Space Invaders ASIC) tt_um_sushi_demo (zc-sushi-demo) tt_um_kch_cd101 (kch cd101) tt_um_uart_bgdtanasa (ttUART) tt_um_zedulo_spitest1 (SimpleSPIdev) tt_um_daobaanh_rng (RNG_test) tt_um_gcd_stephan (15bit GCD) tt_um_spacewar (XY Spacewar) tt_um_gregac_tiny_nn (Tiny Neural Network Accelerator) tt_um_log_afpm (16-bit Logarithmic Approximate Floating Point Multiplier) tt_um_rkarl_Spiral (TT_spiralPattern) tt_um_led_jellyant (ledtest) tt_um_project_tt10 (Simple shift Reg) tt_um_DaDDS (DaDDS) tt_um_nithishreddykvs (Pulse Width Modulation) tt_um_monishvr_fifo (Synchronous FIFO) tt_um_reemashivva_fifo (Asynchronous FIFO) tt_um_save_buffer_hash_table (Tiny Hash Table) tt_um_drum_goekce (DRUM) tt_um_rte_sine_synth (Sine Synth) tt_um_tiny_shader_mole99 (Tiny Shader) tt_um_flummer_ltc (Linear Timecode (LTC) generator) tt_um_bitty (Bitty) tt_um_ole_moller_priority_encoder_to_7_segment_decoder (Priority-encoder) tt_um_algofoogle_vga (IHP VGA demo) tt_um_ultra_tiny_cpu (UltraTiny-CPU) tt_um_uwasic_dinogame (UW ASIC - Optimized Dino) tt_um_Qwendu_spi_fpu (SPI FPU) tt_um_aditya_patra (Priority-Encoded Arbiter) tt_um_4_bit_ALU (ALU) tt_um_htfab_checkers (Overengineered Checkers) tt_um_brukstus_tdc_with_spi (TDC with SPI) tt_um_toniklippeo (toni_clk_gen) tt_um_spi_pwm_djuara (spi_pwm) tt_um_iitbbs (CYCLIPSONIC) tt_um_wokwi_411783629732984833 (BINCounterAndGates) tt_um_wokwi_412635532198550529 (tt09-pettit-wokproc-trainer) tt_um_wokwi_413385294512575489 (Duffy) tt_um_wokwi_413387014781302785 (L display) tt_um_wokwi_413387093939376129 (sphereinabox hello) tt_um_wokwi_413387190167208961 (Will It NAND?) tt_um_wokwi_group_1 tt_um_wokwi_group_2 tt_um_wokwi_group_3 tt_um_wokwi_group_4 tt_um_wokwi_group_5 tt_um_wokwi_group_6 tt_um_wokwi_group_7 tt_um_wokwi_group_8 tt_um_wokwi_group_9 tt_um_wokwi_group_10 tt_um_wokwi_group_11 tt_um_wokwi_group_12 tt_um_tetrap_triggerer (triggerer) tt_um_wokwi_group_13 tt_um_multiplier_group_1 tt_um_multiplier_group_2 tt_um_multiplier_group_3