Gates or IC to use to convert 1x 4 bit 2x 4 bit

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example 1111 = 15 is there a circuit to separate output binaries 0001(1) and 0101(5) in input 1111(15)?
 
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A binary to BCD decoder does what you want. There were the 74LS/HC/HCT185 ICs, but it might be difficult to get one today.
 
my question was to separate 2 binary digits out of the 4 or 5 bit binary. to display it using 2x 7 segment
 
Binary Coded Decimal (BCD) is the same as binary for 0-9, but then it carries to 10 and not to 0A. So this is exactly what you want. A single 74185 chip will decode up to 6 bits of binary to 2 digits of BCD.
(You have to add one or two BCD-7segment decoder/drivers)

Of course you could use a microcontroller or a programmable logic chip, as discussed http://www.electronics-related.com/usenet/basics/show/29703-1.php.

Other alternatives:
- simply use 5 Leds and learn to read binary
- use a BCD-7seg decoder/driver with defined output for input a-f and learn to read this (74247, iirc)
- two digit octal display with two standard BCD-7seg decoder/drivers