2 problems logic design computer science homework help

Q1. A bank vault has four locks with a different key for each lock. One key is owned by the Manager and other keys are owned by the three different employees of the bank. To open the door, the Manager and at least two of the remaining three employees must insert their keys into the assigned locks. The signal lines M, A, B, and C are 1 if there is a key inserted into the locks 1, 2, 3, and 4, respectively. Design a digital circuit using basic gates that would implement the above logic. Hint: This problem is similar to 4.20 (page 117) of your text book.

Q2. A computer interface to a line printer has eight data lines that control the movement of the paper and the print head and determine which character to print. The data lines are labeled A, B, C, D, E, F, G, and H and each represents a binary 0 or 1. When the data lines are interpreted as an 8-bit binary number with line A being the most significant bit, the data lines can represent the numbers 0 to 25510. The number 2310 is the command to return the print head to the beginning of a line, the number 3010 means to advance the paper by one line, and the numbers 6410 to 25510 represent printing characters.

1. (a)  Write an equation for the variable X which is 1 iff the data lines indicate a command to return the print head to the beginning of the line.

2. (b)  Write an equation for the variable Y which is 1 iff there is an advance paper command on the data lines.

3. (c)  Write an equation for the variable Z which is 1 iff the data lines indicate a printable character. (Hint: Consider the binary representations of the numbers 0–63 and 64–255 and write the equation for Z with only two terms)