1. ## Truth Table

3 MOD 4 Function

a. Produce a truth table for a function f of four inputs, a, b, c, d that is 1 when the binary number abcd modulo 4 equals 3, and is 0 otherwise.

b. Produce the corresponding algebraic expression for f.

2. A B C D Output F
0 0 0 0----0
0 0 0 1----0
0 0 1 0----0
0 0 1 1----1
0 1 0 0----0
0 1 0 1----0
0 1 1 0----0
0 1 1 1----1
1 0 0 0----0
1 0 0 1----0
1 0 1 0----0
1 0 1 1----1
1 1 0 0----0
1 1 0 1----0
1 1 1 0----0
1 1 1 1----1

2nd portion use K-MAP you will be able to get the solution. Hope it helps

3. Never learned K-Map???? Is here other way to get the algebraic expression for the truth table.

Would this be correct as the algebraic expression?

f= (¬a.¬b.c.d)+(¬a.b.c.d) +(a.¬b.c.d)+(a.b.c.d)

+ = OR
. = AND

How do I simplify the algebraic form for f as much as possible?

Thanks

4. It is ok if have not learned K-Map. What you are doing is right. Get the minterm and simplify the expression

f = a'b'cd + a'bcd + ab'cd + abcd
f = a'cd(d+d') + acd(b' + b)
f = a'cd +acd
f = cd(a'+a)
f = cd

Using K-Map is much faster but there are certain limitations. You might want to look at that when you have the time.

Karnaugh map - Wikipedia, the free encyclopedia

Hope it helps