1. A computer interface to a line printer has seven data lines that control the movement of the paper and the print head and determine which character to print. The data lines are labeledA,B, C,D,E, F, and G, and each represents a binary o or 1. When the data lines are interpreted as a 7-bit binary number with line A being the most significant bit, the data lines can represent the numbers o to 12710.The number 1310 is the command to return the print head to the beginning of a line, the number 1010 means to advance the paper by one line, and the numbers 3210 to 12710 represent printing characters.

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

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

(c) Write an equation for the variable Z which is 1iff the data lines indicate a printable character. (Hint: Consider the binary representations of the numbers 0-31and 32-127 and write the equation for Z with only two terms.)