Computer Platforms Research Paper Example | Topics and Well Written Essays - 1250 words

Computer Platforms - Research Paper Example 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 2.1 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