Question:

Come up with logic that counts number of ‘1’s in a 7 bit wide vector.You can only use combinational logic.

Answer:

Following is one of the ways to come up with such logic.

Input vector is 7 bit wide. To sum up 7 bits we need 3 bits of binary encoded output.We’ve full adders available. A single full adder can add 3 input bits and generate 2 bitsof binary encoded output.E.g. a full adder can add 3 bit wide input vector ‘111’ and generate ‘11’ output.We can pick two full adders and add up 6 bits of the input vector and will end up withtwo sets of two bit wide binary encoded data.E.g. if input vector is ‘1100111’, we can assume two full adders adding up first 6bits ‘110011’ where first three bits ‘110’ are input to first adder and ‘011’ are inputto second adder. First adder will output ‘10’ (decimal 2) and second adder will alsooutput ‘10’ (decimal 2), and we need to add up two two bit binary vectors. We canagain employ full adders to do this as we still have to account for the 7th input bit ofthe input vector. That can go into the least significant full adder carry-input.

For the above example :

Input vector ‘1100111’

input ‘110’ => full adder => ‘10’ output

input ‘011’ => full adder => ‘10’ output

10

+10

------

100 => output (4)

Now accounting for the seventh input bit ‘1’ as carry into the least significant adder.

1 <= Carry in.

10

+10

-----

101 => Binary encoded decimal 5 which is the input of 1s in inputvector ‘1100111’.

Full adders can be used to add-up 3 input bits at a time. Outputs of first level of fulladders represent the two bit encoded version of the total ‘1’s count, which we need toadd up get the final two digit encoded version of total ‘1’s. Since we need to add up7 bit inputvector, 7th input vector can be used as ‘Carry In’ in the second level of fulladders.