Question

4-6. The Excess-3 coding system is a four-bit digital coding system for encoding all decimal digits from 0 to 9. To encode a decimal digit, we add three to it and then convert the result to binary. A valid code has the following range: 1. Minimum 0011, encoding decimal 0 (0 + 3 310 = 00112) 2. Maximum 1100, encoding decimal 9 (9 + 3 1210 = 11002) Design a logic circuit that will detect an error if a four-bit number is not a valid Excess-3 number. (Hint: Use four input variables to represent the four bits of the Excess-3 number. If the combination = PROBLEMS 243 of the input bits is 0000, 0001, 0010, 1101, 1110, or 1111, the output will be HIGH. For all other cases, the output will be LOW.)

(a) Write a truth table. The input is 4-bit binary ABCD, A is MSB, D is LSB. The output is also represented by x.

(b) Obtain an output expression in the form of a SOP.

(c) Use Boolean Algebra to design a circuit consisting of only four inverters, four 3-input and gate, and one 4-input OR gate using the simplified and simplified expression obtained in (b).

Answer 1

Excess - 3 Numbers Truth Table A B OP 1 0 O 1 o O 2 O 0 1 0 3 4 O | G 1 T 7 7 o 1 0 O 0 0 0 1 o 8 4 0 o 10 1 0 0 1 I 1 12 0 O 13 15 1 K-Map Loop 4. AB OO 01 hoop3 oo 01 1 - Loop I _)) ; 10 ABC+AB D+ ABD+ ABC 2020/10/13 18:36 loop2

off. fi ĀBeta SHABCTABD DABC of Pif 4 NOT Gate 431P AND Gate 14/P OR Gate .