Department of Electrical and Electronic Engineering

EIE2105 Digital and Computer Systems

Tutorial 1: Number Systems, Operations and Codes

1.     Convert the following decimal values into binary.

a.)    20.7510                                             b.)   25.62510

2.     Convert the following binary values into decimal.

a.)    1011.0112                                      b.)    11010.112

3.     Convert the following binary values into hexadecimal.

a.)    1101.1012                                       b.)    101.11012

4.     Convert the following hexadecimal values into decimal.

a.)   AB.C16                                             b.)   45.516

5.     Calculate the following arithmetic operations (show all steps in details). The numbers are 8- bit unsigned integers.

a.)    01110000 × 00000011

b.)   01111000 + 00001111

c.)    01111000 - 00000011

6.     Derive the truth tables of the following Boolean functions, rewrite them in Sum of Minterms and Product of Maxterms, and write down their formal shorthand.

a.) F(A, B, C) = AB + AC

b.) F(A, B, C, D) = AB + AC + BCD + AD

7.     Optimize the following Boolean functions F by K-Map.

a.) F = abcd + abcd + abcd + abcd

with don’t care terms: a bcd , a bcd , a bcd , a bcd , a bcd , a bcd

b.) F = a bcd + a bcd + a bcd

with don’t care terms: a bcd , a bcd , a bcd , a bcd , a bcd , a bcd

c.) F = a bcd + a bcd + a bcd

with don’t care terms: a b c d , a b cd , a bcd , a bcd , a bc d , a bc d