Question

The Boolean expression f (A, B, C, D) is realised with decoders as shown in Figure Q2. A B C D E3=1 74LS138 00 01 3-to-8 02 decoder 03 04 05 06 07 f 00 EN 74LS138 01 0 3-to-8 02 decoder 03 04 05 06 07 (a) Figure Q2 Write down the Boolean expression in ?m() and only use Boolean algebra to simplify the expression. Show your results in sum of product form. All steps must be shown clearly. (8 marks) (b) Implement the simplified Boolean function obtained in Question 2(a) using only 2-input logic gates. Use minimum number of gates. (8 marks) (c) Design the given logic circuit using 8-to-1 multiplexer. Basic gates could be used if needed. Show all the design steps. (9 marks)

          The Boolean expression f (A, B, C, D) is realised with decoders as shown in Figure Q2.
A
B
C
D
E<sub>3</sub>=1
74LS138
0<sub>0</sub>
0<sub>1</sub>
3-to-8
0<sub>2</sub>
decoder
0<sub>3</sub>
0<sub>4</sub>
0<sub>5</sub>
0<sub>6</sub>
0<sub>7</sub>
f
0<sub>0</sub>
EN
74LS138
0<sub>1</sub>
0
3-to-8
0<sub>2</sub>
decoder
0<sub>3</sub>
0<sub>4</sub>
0<sub>5</sub>
0<sub>6</sub>
0<sub>7</sub>
(a)
Figure Q2
Write down the Boolean expression in ?m() and only use Boolean algebra to
simplify the expression. Show your results in sum of product form. All steps must
be shown clearly.
(8 marks)
(b) Implement the simplified Boolean function obtained in Question 2(a) using only
2-input logic gates. Use minimum number of gates.
(8 marks)
(c) Design the given logic circuit using 8-to-1 multiplexer. Basic gates could be used
if needed. Show all the design steps.
(9 marks)

The Boolean expression f (A, B, C, D) is realised with decoders as shown in Figure Q2.
A
B
C
D
E<sub>3</sub>=1
74LS138
0<sub>0</sub>
0<sub>1</sub>
3-to-8
0<sub>2</sub>
decoder
0<sub>3</sub>
0<sub>4</sub>
0<sub>5</sub>
0<sub>6</sub>
0<sub>7</sub>
f
0<sub>0</sub>
EN
74LS138
0<sub>1</sub>
0
3-to-8
0<sub>2</sub>
decoder
0<sub>3</sub>
0<sub>4</sub>
0<sub>5</sub>
0<sub>6</sub>
0<sub>7</sub>
(a)
Figure Q2
Write down the Boolean expression in ?m() and only use Boolean algebra to
simplify the expression. Show your results in sum of product form. All steps must
be shown clearly.
(8 marks)
(b) Implement the simplified Boolean function obtained in Question 2(a) using only
2-input logic gates. Use minimum number of gates.
(8 marks)
(c) Design the given logic circuit using 8-to-1 multiplexer. Basic gates could be used
if needed. Show all the design steps.
(9 marks)

Added by Doris T.

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