1. Convert these binary numbers to decimal. (show your work) a. 10101 b. 10110100 c. 1011100001011...

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1. Convert these binary numbers to decimal. (show your work) a. 10101 b. 10110100 c. 1011100001011 d. 01101101 2. Convert each of the following decimal numbers to hexadecimal. (show your work) a. 47 b. 412 c. 889 d. 512 3. Take each four-bit binary number in the order they are written and write the equivalent hex digit without performing a calculation by hand or by calculator e. 1011 f. 0010 g. 1011 h. 1101 4. Encode these decimal numbers in BCD a. 29 b. 19,585 c. 3456 i. 0000 j. 1100 k. 0111 5. Draw the logic symbol for each of the gates in this section. Use 1 or 2 inputs as appropriate. The first symbol is provided for reference. 5pts. XNOR 6. Fill in the following Truth Tables. 6pts. A A 0 0 0 0 1 1 A 0 0 1 1 B NAND 0 1 0 1 B 0 1 0 1 AND NOT 7. DeMorgan theorem states that a 2-input NOR is equivalent to a 2 (inverted input) AND. Complete the Boolean Expression that expresses that. 3pts. 8. Fill in the Boolean Expression at each output of the logic circuit (drawn to the right). 4pts. First block is filled for you. 9. Fill in the Boolean Expression at each output of the logic circuit (drawn to the right), 4pts. A B [Α] B C 1 1 A 0 0 1 1 AND NAND B 0 1 0 1 B 0 1 0 1 NOR OR OR D NOR A + B = AB A 0 0 1 1 A 0 0 1 1 2 B 0 1 0 1 B 0 1 0 1 XOR XNOR 10. Convert the Boolean Expression into its Logic Circuit. 5pts. Labeling the inputs and outputs will simplify the problem. 11. Convert the Boolean Expression into its Logic Circuit. Labeling the inputs and outputs will simplify the problem. 5pts. 12. At the output of each gate, write the state (0 or 1) of the output. 2pts. 13. At the output of each gate, write the state (0 or 1) of the output. 2pts. A 0 0 1 1 B 0 1 0 1 X = (A + B)C Ā Z-BC+AC 14. Using the Truth Tables below, demonstrate that the Boolean Expression (on the left) is equal. to the Boolean Expression (on the right). 6pts. A(A+B)=AB 0 1 0 A+B A(A+B) A 0 0 1 1 DO B 0 1 0 1 AB 1. Convert these binary numbers to decimal. (show your work) a. 10101 b. 10110100 c. 1011100001011 d. 01101101 2. Convert each of the following decimal numbers to hexadecimal. (show your work) a. 47 b. 412 c. 889 d. 512 3. Take each four-bit binary number in the order they are written and write the equivalent hex digit without performing a calculation by hand or by calculator e. 1011 f. 0010 g. 1011 h. 1101 4. Encode these decimal numbers in BCD a. 29 b. 19,585 c. 3456 i. 0000 j. 1100 k. 0111 5. Draw the logic symbol for each of the gates in this section. Use 1 or 2 inputs as appropriate. The first symbol is provided for reference. 5pts. XNOR 6. Fill in the following Truth Tables. 6pts. A A 0 0 0 0 1 1 A 0 0 1 1 B NAND 0 1 0 1 B 0 1 0 1 AND NOT 7. DeMorgan theorem states that a 2-input NOR is equivalent to a 2 (inverted input) AND. Complete the Boolean Expression that expresses that. 3pts. 8. Fill in the Boolean Expression at each output of the logic circuit (drawn to the right). 4pts. First block is filled for you. 9. Fill in the Boolean Expression at each output of the logic circuit (drawn to the right), 4pts. A B [Α] B C 1 1 A 0 0 1 1 AND NAND B 0 1 0 1 B 0 1 0 1 NOR OR OR D NOR A + B = AB A 0 0 1 1 A 0 0 1 1 2 B 0 1 0 1 B 0 1 0 1 XOR XNOR 10. Convert the Boolean Expression into its Logic Circuit. 5pts. Labeling the inputs and outputs will simplify the problem. 11. Convert the Boolean Expression into its Logic Circuit. Labeling the inputs and outputs will simplify the problem. 5pts. 12. At the output of each gate, write the state (0 or 1) of the output. 2pts. 13. At the output of each gate, write the state (0 or 1) of the output. 2pts. A 0 0 1 1 B 0 1 0 1 X = (A + B)C Ā Z-BC+AC 14. Using the Truth Tables below, demonstrate that the Boolean Expression (on the left) is equal. to the Boolean Expression (on the right). 6pts. A(A+B)=AB 0 1 0 A+B A(A+B) A 0 0 1 1 DO B 0 1 0 1 AB