# mod-5 and Boolean Functions

1) If f is the mod-5 function, compute each of the following.

a) f(17)

b) f(48)

c) f(169)

3) Convert (1011101)2 to base 16 (i.e., hex)

4) Find the sum of products expansion of this Boolean function F(x,y) that equals 1 if and only if x = 1.

Note: one can write out the phrase "y complement" to represent the notation for the complement of y.

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#### Solution Preview

Please see the attached file.

When we apply the function f(q)=qmod(n) to the integer q, the function returns the remainder of the division of q by n:

Now we apply mod(5) to 17.

Since

Dividing 17 by 5 results in 3 and a remainder of 2

Hence:

By this token:

The conversion Table from binary to decimal to hexadecimal ...

#### Solution Summary

This is a set of discrete structures questions involving sum of products, converting to a base, and mod functions.