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Schematic

I've connected a 7447 decoder to 7-segment display as shown in figure. When I connect an input, the LEDs doesn't form numbers but they light up randomly.

I just want to know the right way to connect the output pins of 7447 to the pins of 7-segment display?

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Each segment on a 7-segment display is designated a letter (A-G). This is standard and is shown in the SN7447 datasheet:

enter image description here

You can use a diode tester or a simple voltage source and a resistor to determine the pinout of your particular display. Then just map the pins correctly (again, from datasheet):

enter image description here

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Unless the display is the type that only contains a +1, it should have pinout like this: http://www.alldatasheet.com/datasheet-pdf/pdf/228839/ETC2/FND500.html

Note that this datasheet illustration is a bit messed up and the bottom segment is D (not E), and next segment clockwise (lower left) is E. The 7447 pinout is here:

http://media.digikey.com/pdf/Data%20Sheets/Fairchild%20PDFs/DM7446A,%20DM7447A.pdf

Simply wire the respective letters a..g together (through the 220R resistors). Pin 3 should go to +5 through a 1K resistor. Pin 5 should go to GND.

Note that this is an ancient display and an ancient TTL chip (both are museum old) and because it's TTL open inputs will read as 'high'. You need to tie them to appropriate logic levels (RBI should be '0' if you want to display a zero).

Further, this really old chip saved a few transistors by not fully decoding inputs above 0x09, so 0x0A..0x0F display odd segments here and there (below is from the 74LS47 which has the same logic).

http://www.cs.smith.edu/~thiebaut/270/datasheets/sn74ls47rev5.pdf

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Like the other two most popular answers, your 7 segment display needs to be connected to the 7447 properly (7447 Outputs to Seven-segment display inputs: a-to-a, b-to-b,...,g-to-g). However, they don't seem to mention that you need to have the inputs of the 7447 connected to something for it to work like you want it to. Namely, you need a decade counter that outputs the numbers 0-9 in Binary-Coded-Decimal and those outputs connect to the 4 A, B, C, & D inputs on the left side of your 7447. Also to funct5ion as a clock the 7490 (decade counter) needs a clock pulse provided by a 555 timer and the 7447 needs its Lamp-Test (LT) & Blanking Input (BI) set to V-Supply (High or 5V for a 7447) and the Latch Enable (LE) input set to 0V or GND.

WIRING (EXCLUDING PSU CONNECTIONS (ONLY WIRING BETWEEN CHIPS AND 555 TIMER EXTERNAL COMPONENTS FOR TIMING)

Here is a schematic from Forrest Mims Engineer's Notebook (LLH-Publishing, 1992) P.59: Forrest Mims III's Engineer's Notebook (LLH-Publishing, 1992) P.59

Here is a link to a video I made on instagram of mine working using this schematic: https://photos.app.goo.gl/70R7aPXTkkexWE6K2

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