using Venn diagrams
using truth tables
using Boolean algebra.
| 1) | a) | Write the following decimal numbers as binary numbers to 12-bit accuracy | |
|---|---|---|---|
| (i) 1562.5 (ii) 348.678 (iii) 74.8063 | |||
| b) | Write the following hexadecimal numbers as decimal numbers | ||
| (i) 7BA (ii) A25C (iii) C2.57 | |||
| c) | Write the following decimal numbers as BCD coded binary numbers | ||
| (i) 26 (ii) 527 | |||
| d) | Write the Gray-coded equivalent of decimal 37. | ||
| e) | Convert the Gray-coded number 1001101101 to its binary equivalent. | ||
| 2) | a) | Prove the Boolean expression using Venn diagrams | |
| b) | Prove the Boolean expression using truth tables | ||
| c) | Verify using Boolean algebra. | ||
| 3) | A modulo-16 ripple counter has a clock frequency of 3.33MHz and the intrinsic timing delay for each Flip-Flop is 75ns. | ||
| a) | Draw an accurate timing diagram for this circuit, consider the first 5 full clock pulses only. | ||
| b) | Add to your timing diagram the output from the ripple counter (as a decimal number) for each change in the output. | ||
| 4) | A sequential logic circuit is constructed as below | ||
| |||
| the output of the circuit, F, is fed back to form an internal input F' (note the use of the invert bubbles on the inputs to the AND gate) | |||
| a) | Give the Boolean expression for this circuit. | ||
| b) | Develop the truth table for this circuit. | ||
| c) | Indicate the stability of each row in the truth table. | ||
| d) | Summarise the behaviour of the circuit with a flow table. | ||
| e) | Describe what happens to the circuit as the inputs switch from AB=11 to AB=01. | ||
| f) | What is happening to the output F when AB=00? | ||