# Tutorial 1 - katzen.me.uk

```University of Ulster
School of Electrical &amp; Mechanical Engineering
EEE111J2 Digital Systems &amp; Microprocessors
(Digital Systems Tutorials)
Tutorial 1
Q.1 In the diagram below the waveform shown is periodic, with the two waves shown being
identical.
90%
Linear
50%
Linear
50%
12 ns
10%
tW
2 ns
(i)
(ii)
(iii)
Q.2
Calculate the Period, T, in nano-seconds.
Calculate the frequency, f, in Hertz.
Calculate the Duty Cycle as a percentage.
(i)
44 ns, (ii)
22.72 MHz (2dp), (iii) 31.81%
(a) 57 (b) 107
(c) 87
(d) 51.75
(e) 42.25
(f) 92.65625
Convert the following decimal numbers and decimal fractions to binary:
(a) 61
(b) 93
(c) 186
(d) 0.98
(e) 0.347
(f) 0.9028
Q.3
30 ns
Convert the following binary numbers to decimal:
(a) 111001
(b) 1101011
(c) 1010111
(d) 110011.11
(e) 101010.01
(f) 1011100.10101
Q.3
3 ns
(a) 111101
(b) 1011101 (c) 10111010 (d) 0.11111010
(e) 0.01011001 (f) 0.11100111
Perform the following operations on binary numbers as indicated by the arithmetic sign.
(a) 111 + 110
(b) 1011 + 101
(c) 1101 + 1011
(d) 1110 – 11
(e) 1100 – 1001
(f) 11010 – 10111
(g) 1001 &times; 110
(h) 1101 &times; 1101
(i) 1110 &times; 1101
(c) 11000
(d) 1011
(g) 1100110 (h) 10101001 (i) 10110110
(e) 11
(f) 11
Q.4
Determine the 2’s complement of each binary number.
(a) 11100
(b) 10111
(c) 10110000 (d) 00111101
Q.5
(c) 01010000 (d) 11000011
Express each decimal number as an 8-bit number in 2’s complement system.
(a) +12
(b) –68
(c) +101
(d) –125
Answer: (a) 00001100 (b) 10111100 (c) 01100101 (d) 10000011
Q.6
Determine the decimal value of each signed binary number in 2’s complement system.
(a) 10011001
(b) 01110100
(c) 10111111
Q.7
(b) +116
(c) –65
Convert each pair of decimal numbers to binary and add using 2’s complement system.
(a) 33 and 15 (b) 56 and –27 (c) –46 and 25 (d) –110 and –84
Answers: (a) 00110000 (b) 00011101 (c) 11101011 (d) 100111110
Q.8
Convert each hexadecimal number to binary:
(a) 3816
(b) 5916
(c) A1416
(d) 5C816
(b) 01011001
(e) 11111101100011111
Q.9
(c) 101000010100 (d) 010111001000
Convert each binary number to hexadecimal:
(a) 10111 (b) 10100110
(c) 1111110000
(b) A616
(c) 3F016
(e) FB1716
(d) 100110000010
(d) 98216
Q.10
Convert each hexadecimal number to decimal:
(a) 2316
(b) 1A16
(c) F316
(d) 5C216
(a) 35
(b) 26
(c) 243
(d) 1474
Q.11
Convert each decimal number to hexadecimal:
(a) 14
(b) 52
(c) 284
(d) 4019
(e) 6500
(a) E16
(b) 3416
(c) 11C16
(d) 196416
Q.12
(b) A016 + 6B16
(a) 3716 + 2916