A logical network has 4 inputs (A, B, C, D) and one output (Z). The four inputs together represent the N 4 bits long binary number ( „A” input  is the most significant bit). The output must be logical 1, if:

1st DIGITAL DESIGN HOMEWORK (3)

1st problem:

• Count the hexadecimal equivalent of the decimal 777.654. The fractional part of the binary number must be 4 bits accurate.

(method : decimal è binary è hexadecimal)

• Count the decimal equivalent of the binary number 1110 0111.1101 !

2nd problem:

The F logical function depends on 3 variables.  F (A,B,C) = ∑³ (0,5,6).

• Define algebraic canonical disjunctive form of the function !
• Count the maxterm-vector of the function!
• Define algebraic canonical conjunctive form of the function !

3rd problem:

A logical network has 4 inputs (A, B, C, D) and one output (Z). The four inputs together represent the N 4 bits long binary number ( „A” input  is the most significant bit). The output must be logical 1, if:

• N < 15, and N is odd, or
• N < 3 and N is even, or (  N=0 is even!)
• N=10.

Tasks:

• Fill the truth table of this function !
• Count the minterm and maxterm vectors of the function!
• Simplificate the function, find the simplest disjunctive function ! Apply the GRAPHICAL simplification!
• Simplificate the function, find the simplest disjunctive function ! Apply the NUMERICAL simplification!
• Realize it based on AND and OR gates !