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[ECEN 1400] Introduction to Digital and Analog Electronics R. McLeod HW #6: Counters and Binary Math 1 Conversion Practice (5pts) • Fill in the table by writing the same number in each row using the bases specified. • Use a subscript indicates the base. • For example 102 = 210 = 216 and 100002 = 1610 = 1016 Binary Decimal 9910 Hexadecimal 1110112 E716 19510 101010102 2 Same Problem, Two Bases (5pts) Square the number 110011002 by doing long multiplication in binary. That is, multiply each element in one number by a single digit in the other number and write the result shifted left by the position of the digit, then add the columns with appropriate carry. (3 pts). Then convert the original number and the answer to decimal (2 pts) and check the result. 3 Mixed Base Multiplication and Division (5pts) Perform the specified operation and write the result in the specified base. a 100110102 10102 10102 3210 101100102 4 Operation ÷ × × ÷ × b 210 410 1016 1016 1610 = In Base 2 2 16 2 16 Cascaded 74161 Counters (35pts) Create a 4 bit counter in multisim using the 74HC163N 4V counter (CMOS → 74HC 4V → 74HC163N 4V). This is not precisely the chip we will use the in the lab, but has sufficiently similar processes. Look at the datasheet and the lecture notes to understand the function of the chip. Connect pins 7, 10, 9 and 1 to +5V and a function generator (Simulate → Instruments → Function generator) to pin 2, the clock. Set the function generator to a 32 KHz square wave with 2.5 Vp (not peak to peak) amplitude and 2.5 V offset such that the voltage is swinging from 0 to 5V. Wire Common to ground and + to the counter clock input. Your function generator dialog box should look like: Version 3.2, October 15, 2014 Page 1 [ECEN 1400] Introduction to Digital and Analog Electronics R. McLeod Show your circuit with a screen shot. Examine the outputs of QA, QB, QC, QD with a scope (Simulate → Instuments, then pick your favorite; The Tek scope has 4 inputs, which is nice) to confirm that they are at the expected frequencies relative to the clock input. Examine the input clock, QA, QD and RCO. Can you write a logic expression for RCO? Is this chip triggered on the falling or rising edge of the clock? Now copy and paste a second counter to the right of the first, wiring pints 1,9,10 and 7 the same way. Connect QD from counter 1 to CLK (pin 2) of the new counter. Now examine the outputs QA, QB, QC, QD of counter 2 and again confirm that they are at the expected frequencies. The simulation will run a bit slowly give the large range of time-scales in the circuit. How many effective bits are in your combined counter? How many clock cycles occur before RCO on the second counter signals that this counter has rolled over? Version 3.2, October 15, 2014 Page 2