1. 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

2. Problems (Mano)
Obtain the simplified Boolean expressions for outputs F and G in terms of the input variables in (A,B,C and D)

3. Problems (Mano)

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. Problem (Mano)
Design a combinational circuit that converts a four bit Gray code to four bit binary number

17. Problem (Mano)
Design a combinational circuit that converts a four bit Gray code to four bit binary number

18. Problem (Mano)
Design a combinational circuit that converts a four bit Gray code to four bit binary number

19. Problem (Mano)
Design a combinational circuit that converts a four bit Gray code to four bit binary number

20. Example: Three 1s Detector
Problem: Detect three consecutive 1s in 8-bit input: abcdefgh
   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

21. Example: Number of 1s Count
Problem: Output in binary on two outputs yz the number of 1s on three inputs
010    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