Lecture 13 Problems (Mano) Give qualifications of instructors: DAP teaching computer architecture at Berkeley since 1977 Co-athor of textbook used in class Best known for being one of pioneers of RISC currently author of article on future of microprocessors in SciAm Sept 1995 RY took 152 as student, TAed 152,instructor in 152 undergrad and grad work at Berkeley joined NextGen to design fact 80x86 microprocessors one of architects of UltraSPARC fastest SPARC mper shipping this Fall
Problems (Mano) Obtain the simplified Boolean expressions for outputs F and G in terms of the input variables in (A,B,C and D)
Problems (Mano)
Design a combinational circuit with three inputs and one output Problem (Mano) Design a combinational circuit with three inputs and one output The output is 1 when binary value of the inputs is less than 3, the output is zero otherwise The output is 1 when binary value of the inputs is an odd number
Design a combinational circuit with three inputs and one output Problem (Mano) Design a combinational circuit with three inputs and one output The output is 1 when binary value of the inputs is an odd number
Problem (Mano) Design a combinational circuit with three inputs x, y and z and three outputs A, B and C, when the binary input is 0, 1, 2 or 3, the binary output is two greater than the input. When the binary input is 4, 5, 6 or 7, the binary output is three less than the input
Problem (Mano) Design a combinational circuit with three inputs x, y and z and three outputs A, B and C, when the binary input is 0, 1, 2 or 3, the binary output is two greater than the input. When the binary input is 4, 5, 6 or 7, the binary output is three less than the input
Problem (Mano) Design a combinational circuit with three inputs x, y and z and three outputs A, B and C, when the binary input is 0, 1, 2 or 3, the binary output is two greater than the input. When the binary input is 4, 5, 6 or 7, the binary output is three less than the input
Problem (Mano) An ABCD-to-seven segment decoder is a combinational circuit that converts a decimal digit in BCD to an appropriate code for the selection of segments in an indicator used to display the decimal digit in a familiar form. The seven outputs of the decoder (a, b, c, d, e, f, g) select the corresponding segment in the display as shown in Fig. The numeric display chosen to represent the decimal digit is also shown in Fig. Using the truth table and K-Map, design the BCD-to-seven-segment decoder using the minimum number of gates
Problem (Mano) An ABCD-to-seven segment decoder is a combinational circuit that converts a decimal digit in BCD to an appropriate code for the selection of segments in an indicator used to display the decimal digit in a familiar form. The seven outputs of the decoder (a, b, c, d, e, f, g) select the corresponding segment in the display as shown in Fig. The numeric display chosen to represent the decimal digit is also shown in Fig. Using the truth table and K-Map, design the BCD-to-seven-segment decoder using the minimum number of gates
Problem (Mano) An ABCD-to-seven segment decoder is a combinational circuit that converts a decimal digit in BCD to an appropriate code for the selection of segments in an indicator used to display the decimal digit in a familiar form. The seven outputs of the decoder (a, b, c, d, e, f, g) select the corresponding segment in the display as shown in Fig. The numeric display chosen to represent the decimal digit is also shown in Fig. Using the truth table and K-Map, design the BCD-to-seven-segment decoder using the minimum number of gates
Problem (Mano) An ABCD-to-seven segment decoder is a combinational circuit that converts a decimal digit in BCD to an appropriate code for the selection of segments in an indicator used to display the decimal digit in a familiar form. The seven outputs of the decoder (a, b, c, d, e, f, g) select the corresponding segment in the display as shown in Fig. The numeric display chosen to represent the decimal digit is also shown in Fig. Using the truth table and K-Map, design the BCD-to-seven-segment decoder using the minimum number of gates
Problem (Mano) An ABCD-to-seven segment decoder is a combinational circuit that converts a decimal digit in BCD to an appropriate code for the selection of segments in an indicator used to display the decimal digit in a familiar form. The seven outputs of the decoder (a, b, c, d, e, f, g) select the corresponding segment in the display as shown in Fig. The numeric display chosen to represent the decimal digit is also shown in Fig. Using the truth table and K-Map, design the BCD-to-seven-segment decoder using the minimum number of gates
Problem (Mano) An ABCD-to-seven segment decoder is a combinational circuit that converts a decimal digit in BCD to an appropriate code for the selection of segments in an indicator used to display the decimal digit in a familiar form. The seven outputs of the decoder (a, b, c, d, e, f, g) select the corresponding segment in the display as shown in Fig. The numeric display chosen to represent the decimal digit is also shown in Fig. Using the truth table and K-Map, design the BCD-to-seven-segment decoder using the minimum number of gates
Problem (Mano) An ABCD-to-seven segment decoder is a combinational circuit that converts a decimal digit in BCD to an appropriate code for the selection of segments in an indicator used to display the decimal digit in a familiar form. The seven outputs of the decoder (a, b, c, d, e, f, g) select the corresponding segment in the display as shown in Fig. The numeric display chosen to represent the decimal digit is also shown in Fig. Using the truth table and K-Map, design the BCD-to-seven-segment decoder using the minimum number of gates
Problem (Mano) Design a combinational circuit that converts a four bit Gray code to four bit binary number
Problem (Mano) Design a combinational circuit that converts a four bit Gray code to four bit binary number
Problem (Mano) Design a combinational circuit that converts a four bit Gray code to four bit binary number
Problem (Mano) Design a combinational circuit that converts a four bit Gray code to four bit binary number
Example: Three 1s Detector Problem: Detect three consecutive 1s in 8-bit input: abcdefgh 00011101 1 10101011 0 11110000 1 Step 1: Capture the function Truth table or equation? Truth table too big: 28 = 256 rows Equation: create terms for each possible case of three consecutive 1s y = abc + bcd + cde + def + efg + fgh Step 2: Convert to equation -- already done Step 3: Implement as a gate-based circuit bcd def fgh abc cde efg y a b c d e f g h
Example: Number of 1s Count Problem: Output in binary on two outputs yz the number of 1s on three inputs 010 01 101 10 000 00 Step 1: Capture the function Truth table or equation? Truth table is straightforward Step 2: Convert to equation y = a’bc + ab’c + abc’ + abc z = a’b’c + a’bc’ + ab’c’ + abc Step 3: Implement as a gate-based circuit a b c z a b c y