A binary input of 0100 would light four LEDs in a row whilst a binary input of 0101 would light five LEDs in a row. Derive the truth-table for a 4 bit input/ 16 bit output decoder which would be used to power this linear display.

Solution: Let x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14 and x15 represent the linear array of LEDs. Let A, B, C and D represent the binary input terminals. The truth-table for the linear display is shown in Figure 2.2.

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Table 2.1 gives details as to which segments should be energised to display various decimal values at the 4-pin input.

Decimal

A

B

C

D

Segments

0

0

0

0

0

a, b, c, d, e, f

1

0

0

0

1

b, c

2

0

0

1

0

a, b, g, e, d

3

0

0

1

1

a, b, c, d, g

4

0

1

0

0

b, c, f, g

5

0

1

0

1

a, c, d, f, g

6

0

1

1

0

c, d, e, f, g

7

0

1

1

1

a, b, c

8

1

0

0

0

a, b, c, d, e, f, g

9

1

0

0

1

a, b, c, f, g

Table 2.1 Truth-table for BCD-to-seven-segment decoder

Hence we can derive expressions for each segment, as follows:

a = A'B'C'D' + A'B'CD' + A'B'CD + A'BC'D + A'BCD + AB'C'D' + AB'C'D

b = A'B'C'D' + A'B'C'D + A'B'CD' + A'B'CD + A'BC'D' + A'BCD + AB'C'D' + AB'C'D

c = A'B'C'D' + A'B'C'D + A'B'CD + A'BC'D' + A'BC'D + A'BCD' + A'BCD + AB'C'D'

+ AB'C'D

d = A'B'C'D' + A'B'CD' + A'B'CD + A'BC'D + A'BCD' + AB'C'D'

e = A'B'C'D' + A'B'CD' + A'BCD' + AB'C'D'

f = A'B'C'D' + A'BC'D' + A'BC'D + A'BCD' + AB'C'D' + AB'C'D

g = A'B'CD' + A'B'CD + A'BC'D' + A'BC'D + A'BCD' + AB'C'D' + AB'C'D

2.b A display composed of a linear array of LEDs, is to respond to a 4-bit binary input which is dependent on the absolute binary value by lighting each successful element. A binary input of 0100 would light four LEDs in a row whilst a binary input of 0101 would light five LEDs in a row. Derive the truth-table for a 4 bit input/ 16 bit output decoder which would be used to power this linear display.

Solution: Let x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14 and x15 represent the linear array of LEDs. Let A, B, C and D represent the binary input terminals. The truth-table for the linear display is shown in Figure 2.2.

Table 2.2 Truth-table for LEDs of linear display

3.a The decimal number 101 may be represented in binary as 01100101. Using One's
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