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Specify the size of a ROM (number of words and number of bits per word) that will accommodate the truth table for the following combinational circuit :

a code converter from a 4-digit BCD number to a binary number.

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in the question code converter from a 4-digit BCD number is mention ,

Now , the table for code converter have 16 rows , hence total 24 = 16 combinations are there and each combination correspond to a 14 bit binary number. The size for converter table is 216 

Total size of ROM required (216   *  14 ) as each combination is 14 bits long.

Same type of question  -->  https://gateoverflow.in/26836/rom-size-to-build-adder-substractor

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Refresher:

Binary-coded decimal (BCD) is a class of binary encodings of decimal numbers.

Eg: 1001 in BCD representation represents decimal no. 9

       1001 1001 in BCD representation represents decimal no. 99 and so on.

Doubt Clarification:

//Note: I/P is in BCD, Output is in Binary.

1 digit BCD input, binary output:

     Max possible I/p: 1001 (9)     O/P: = 1001 (9)

      Input lines eqd.     = 4  

      Output lines reqd. = 4


2 digit BCD input, binary output:

     Max possible I/p: 1001 1001 (99)  O/P: 1100011(99)

      Input lines reqd.     = 8     //count the no. of input bits

      Output lines reqd. =  7     // ceil (log 99) = ceil (6.6293) = 7

                                                //or simply count the no. of output bits


3 digit BCD input, binary output:

     Max possible I/p: 1001 1001 1001 (999)  O/P: 1111100111(999)

      Input lines eqd.     = 12

      Output lines reqd. =  10     // ceil (log 999) = ceil (9.964) = 10


4 digit BCD input, binary output:

     Max possible I/p: 1001 1001 1001 1001 (9999)  O/P: 10011100001111(9999)

      Input lines eqd.     = 16

      Output lines reqd. =  14     // ceil (log 9999) = ceil (13.28) = 14

Hence, Size of ROM with 16 input lines and 14 output lines is: 2^16 * 14 bits

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