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

Answer:

The output is 1 for:

$1_{10} = (0001)_{2}$

$2_{10} = (0010)_{2}$

$3_{10} = (0011)_{2}$

$5_{10} = (0101)_{2}$

$7_{10} = (0111)_{2}$

$11_{10} = (1011)_{2}$

$13_{10} = (1101)_{2}$

Step-by-step 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