Question

13.4

LIRIY WILL Write a DUI expeSSIUI IUI ed UL ce su u 13.4 We need a logic circuit that gives an output logic signal X which is high when an error in the form of an unused code occurs in a given BCD codeword. The inputs to the logic circuit are the bits B3, B4, B, and B, of the BCD codeword. Start by constructing a truth table for X. Then K-map it and go from there, whistling while you work. 12 Nacion. Rondanimal (1.f.101 dernder using logic gates

Answer 1

So according to question our objective is to make a function X that output high when an unused codeword occurs in input and for all correct BCD inputs it outputs low.

So we will make truth table Now using 4 inputs B₈, B₄, B₂, B₁, and output X. We will mark all non BCD codeword in output as 1 and other inputs as 0. All codeword from 0-9 is marked as 0 in output and 10-15 as 1.

Truth Table:

B8	B4	B2	B1	X
0	0	0	0	0
0	0	0	1	0
0	0	1	0	0
0	0	1	1	0
0	1	0	0	0
0	1	0	1	0
0	1	1	0	0
0	1	1	1	0
1	0	0	0	0
1	0	0	1	0
1	0	1	0	1
1	0	1	1	1
1	1	0	0	1
1	1	0	1	1
1	1	1	0	1
1	1	1	1	1

Let us make K-map for this truth table

We have 6 minterms in X given below

x = Em (10, 11, 12, 13, 14, 15) B8 By oo ol 1 10 So Two implicants mutmiot mint mis-B8B2 01 mi2+ m 13+ Mly this = B8 By 11 x is sum of these two x= B8 B2 + Bo By 10 x = Bo (Br + Bu) is minimum Sop af x. This

So finally we have the expression for X

X = B (B2+ B4)

Logic Circuit for expression is given below

B2+ By - x = (B2+ B4) BB