Question

Create a truth table of the function PRIME(A,B,C,D) where A,B,C,D are the bits of a 4-bit number. A is the highest significant bit and D is the least significant.

Answer 1

The output is 1 for:

`1_(10) = (0001)_(2)`

`2_(10) = (0010)_(2)`

`3_(10) = (0011)_(2)`

`5_(10) = (0101)_(2)`

`7_(10) = (0111)_(2)`

`11_(10) = (1011)_(2)`

`13_(10) = (1101)_(2)`

Explanation:

The first step is creating the truth table, from the most significant bit to the least significant. Then, each value is converted to decimal, like these two examples:

`(1111)_(2) = 1*2^(0) + 1*2^(1) + 1*2^(2) + 1*2^(3) = 15`

`(1110)_(2) = 0*2^(0) + 1*2^(1) + 1*2^(2) + 1*2^(3) = 14`

After the conversion, if the decimal equivalent of the 4-bit number is prime, the output is 1.

So, the output is 1 for 1,2,3,5,7,11,13

So

A - B - C - D - Decimal - Output

0 - 0 - 0 - 0 - 0 - 0

0 - 0 - 0 - 1 - 1 - 1

0 - 0 - 1 - 0 - 2 - 1

0 - 0 - 1 - 1 - 3 - 1

0 - 1 - 0 - 0 - 4 - 0

0 - 1 - 0 - 1 - 5 - 1

0 - 1 - 1 - 0 - 6 - 0

0 - 1 - 1 - 1 - 7 - 1

1 - 0 - 0 - 0 - 8 - 0

1 - 0 - 0 - 1 - 9 - 0

1 - 0 - 1 - 0 - 10 - 0

1 - 0 - 1 - 1 - 11 - 1

1 - 1 - 0 - 0 - 12 - 0

1 - 1 - 0 - 1 - 13 - 1

1 - 1 - 1 - 0 - 14 - 0

1 - 1 - 1 - 1 - 15 - 0