Count number of logic 1's in 7 bit number

Discussion in 'Homework Help' started by ppd, Feb 11, 2011.

1. ppd Thread Starter New Member

Feb 11, 2011
2
1
What is the simplest logic circuit to count the number of logic ones in a 7 bit input, using only half adders and full adders?

2. Georacer Moderator

Nov 25, 2009
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Since you will be using adders, try to see the operation as a sum of numbers. You have 7 numbers, the figures of your 7-bit number. All 7 numbers are 1-bit long. Let's name the figures of your number b0-b6, from the LSB to the MSB. Let's break down the operation:

Using a 1-bit Full Adder you can add 3 1-bit numbers (1st summand, 2nd summand, Carry-in) and get a 2-bit number.
Thus you can sum b0,b1,b2 with one FA, and b3,b4,b5 with a second FA.

You now have 2 2-bit numbers and one 1-bit number, the b6.

Using a 2-bit FA (which is made of 2 1-bit FA), you can add 2 2-bit numbers and 1 1-bit number (the carry in). You already have the 2 2-bit numbers as the result of the 2 previous additions, and the b6 will be used as the carry-in.
In the end, you end up wit 1 3-bit number, which can have a maximum value of 7.

In that implementation we used 4 Full Adders.

Is that clear?

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3. ppd Thread Starter New Member

Feb 11, 2011
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That was perfectly clear. Thank you!

Tirumala likes this.

Nov 25, 2009
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