Question

Consider the following four types of gates: AND, OR, NAND and NOR. If we assign one type of gate for the first level and one type for the second level, we find that there are 16 possible combinations of two-level forms. Eight of these combinations are said to be degenerate forms because they result in a single Boolean operation. List these eight degenerate combinations and show why this is the case, resulting in extending the number of inputs to a gate. Include a labeled (inputs and outputs at each stage) circuit diagram for each case. (Non-degenerate forms are listed at the bottom of pg. 98 of the textbook.) (Use Logisim “Export Image” for all circuit diagrams)

Answer 1

If the output of two level logic realization can be obtained by using single Logic gate, then it is called as degenerative form.

SINCE, in degenerate form, the two level gate circuit can be represented by a single Logic Gate, but we will need input of both the logic gates must be given to a single gate, in this way, it extends the number of inputs to a gate.

There are 8 degenerate forms present:

AND-AND, OR-OR, AND-NAND, OR-NOR, NAND-OR, NOR-AND, NOR-NAND, NAND-NOR

AND - NAND AND-AND CAB) CD) A B 46 (c o C.D a c. A BLO AB CO OR-OR A 18) 4. A+B 8 (c+D) 13 (A18+ +0)

A :8) A. CA8' C. (co) output 3 (AA), → (er), 8 NAND -NO (Ae) 8 (co) i

NOR-AND 6 C+ D) CAtC) CC+ D) 0 2 A+84) ナ(C+0) (MB)"(C4D)) ブ

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