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KMIC 2008-2009
Numeral Systems

1.1 Binary Numeral Systems

1.1.1 Conversions

Task 1.1.1.1
Convert decimal number (1584)d into its binary format.

Solution:
Decimal to Binary Conversion
Task 1.1.1.2
Convert decimal number (0.625)d into its binary format.

Solution:
Decimal to Binary Conversion
Task 1.1.1.3
Convert decimal number (0.3)d into its binary format.

Solution:
Decimal to Binary Conversion
Task 1.1.1.4
Convert decimal number (14.6875)d into its binary format.

Solution:
Decimal to Binary Conversion
Task 1.1.1.5
Convert binary number (101010001.10001)b into its decimal format.

Solution:
Binary to Decimal Conversion

1.1.2 Addition

Table of rules
Term Result Carry
0+0 0 0
0+1 1 0
1+0 1 0
1+1 0 1
1+1+1 1 1

Task 1.1.2.1
Calculate: (10101000)b+(00111101)b.

Solution:
Binary Addition
Task 1.1.2.2
Calculate: (10101111)b+(11010101)b.

Solution:
Binary Addition

1.1.3 Subtraction

Table of rules
Term Result Borrow
0-0 0 0
1-0 1 0
1-1 0 0
0-1 1 1
0-1-1 0 1

Task 1.1.3.1
Calculate: (10111011)b-(00100101)b.

Solution using Binary Subtraction:
Binary Subtraction
Solution using Two's Complement:
Two's complement of the number (00100101)bis:

Two's Complement
Calculating (10111011)b-(00100101)b is the same as adding (10111011)b and two's complement of the number (00100101)b:
Two's Complement subtraction
Task 1.1.3.2
Calculate (78)d - (116)d.

Solution using Two's Complement:
(116)d = (01110100)b
(78)d = (01001110)b

Two's complement of the number (01110100)b is:
Binary Subtraction


Zpět 
Mail Address   Ústav automatizace a měřicí techniky, VUT v Brně
Kolejní 2906/4, 612 00 Brno, Czech Republic
Phone   (+420) 541141154
Fax   (+420) 541141123
     
Last Update: 08/08/2008
By: kucera@feec.vutbr.cz