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ECE 320 Homework #3. Simplify the Boolean function F using the don’t care conditions d, in both S.O.P. and P.O.S. form: F=A’B’D’+A’CD+A’BC d=A’BC’D+ACD+AB’D’ F=W’(X’Y+X’Y’+XYZ)+X’Z’(Y+W) d=W’X(Y’Z+YZ’)+WYZ F=ACE+A’CD’E’+A’C’DE d=DE’+A’D’E+AD’E’ F=B’DE’+A’BE+B’C’E’+A’BC’D’
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ECE 320 Homework #3 • Simplify the Boolean function F using the don’t care conditions d, in both S.O.P. and P.O.S. form: • F=A’B’D’+A’CD+A’BC d=A’BC’D+ACD+AB’D’ • F=W’(X’Y+X’Y’+XYZ)+X’Z’(Y+W) d=W’X(Y’Z+YZ’)+WYZ • F=ACE+A’CD’E’+A’C’DE d=DE’+A’D’E+AD’E’ • F=B’DE’+A’BE+B’C’E’+A’BC’D’ d=BDE’+CD’E’
ECE 320 Homework #3 • Analyze the two output circuit shown in Figure below. Indicate the logical expression associated with every gate output. C F A B Z
ECE 320 Homework #3 • A 4-bit BCD number in 84-2-1 code is to be checked to determine whether the 4-bits represent the valid BCD number. Develop a minimum-gate-count combinational checking circuit whose output will be a 1 if the input is not a valid BCD number otherwise it will be a zero. • A BCD-to-seven-segment decoder is a combinational circuit that accepts a decimal digit in BCD and generates the appropriate outputs for selection of segments in a display indicator used for displaying the decimal digit. The seven outputs of the decoder (a,b,c,d,e,f,g) select the corresponding segments in the display as
ECE 320 Homework #3 5. shown in Figure (a). The numeric designation chosen to represent the decimal digit is shown in Figure (b). Design the BCD-to-seven-segment decoder circuit. (a) Segment Designation (b) Numeric Designation
