University of Ulster
School of Electrical & Mechanical Engineering
EEE111J2 Digital Systems & 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)
Answers:
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
Answers:
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
Answers:
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 × 110
(h) 1101 × 1101
(i) 1110 × 1101
Answers: (a) 1101 (b) 10000
(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
Answers: (a) 00100 (b) 01001
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
Answers: (a) –103
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
Answers: (a) 00111000
(b) 01011001
(e) 11111101100011111
Q.9
(c) 101000010100 (d) 010111001000
Convert each binary number to hexadecimal:
(a) 10111 (b) 10100110
(c) 1111110000
Answers: (a) 1716
(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
Answers:
(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
Answers:
(a) E16
(b) 3416
(c) 11C16
(d) 196416
Q.12
Perform the following additions:
(b) A016 + 6B16
(a) 3716 + 2916
Answers: (a) 7016
(b) 10B16
(c) 1BA16
Perform the following subtractions:
(a) 5116 - 4016
(b) C816 – 3A16
Answers: (a) 1116
(b) 8E16
(c) 7516
(c) FF16 + BB16
Q.13
(c) FD16 - 8816