2. Introduction to Decimal Number System:
A positional system of numeration that uses decimal digits and a base
ten. The number system we use every day, based on 10 digits
(0,1,2,3,4,5,6,7,8,9) position is important.The decimal numeral
system (also called base ten or occasionally denary) has ten as its
base. It is the numeral base most widely used by modern civilizations.
Binary Number System:
A method of representing number that has 2 as its base and uses only
the digits 0 and 1.Number system that uses only two values (0,1) to
represent codes and data. Since zeros and ones can be easily
represented by two voltages. The binary system is the foundation on
which digital technology is built. Every digital computer whether a
pocket calculator or a mainframe uses the same binary notation.
16. Exercise-1.1
1. Convert the following decimal numbers into equivalent binary
numbers.
i) 32 ii) 57 iii) 67
iv) 89 v) 185 vi) 369
vii) 412 viii) 567 ix) 1853
x) 3922
2. Convert the following decimal fraction into equivalent binary
fractions.
i) 0.125 ii) 0.625 iii) 0.5625
iv) 0.859375 v) 0.078125
3. Convert the following binary numbers into equivalent decimal
numbers.
i) 101 ii) 1000 iii) 1001
iv) 1011 v) 1100 vi) 100001
vii) 1000001 viii) 1010001 ix) 10011101
x) 111000011
17. 4. Convert the following binary fraction into decimal fractions.
i) 0.001 ii) 0.101 iii) 0.1001
iv) 0.110111 v) 0.000101
5. Convert the following decimal into binary fractions.
i) 25.125 ii) 412.5625
6. Convert the following binary into decimal fractions.
i) 111001.101 ii) 10111001.000101