(a) Conversion of decimal number (259.8125)10 into hexadecimal form
(b) Conversion of hexadecimal number B2F.5 into Decimal equivalent.
► When hexadecimal is used to represent a binary number, the individual hexadecimal digits represent successive groups of four binary digits starting at the point. This is similar to the conversion from binary to octal, in which each set of three bits is translated to an octal digit.
Arithmetic of Number Systems:
Number System Base Digit Used
Binary 2 0,1
Octal 8 0,1,2,3,4,5,6,7
Decimal 10 0,1,2,3,4,5,6,7,8
Hexadecimal 16 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
Arithmetic Operations of Binary Numbers:
► In the Binary System, there are only two symbols or possible digit values, i.e., 0 and 1. Represented by any device that only 2 operating states or possible conditions. Generally, it is expressed by subscript 2 or binary (B).
► Binary arithmetic is essential part of various digital systems. You can add, subtract, multiply, and divide binary numbers using various methods. These operations are much easier than decimal number arithmetic operations because binary system has only two digits: 0 and 1.
► Binary additions and subtractions are performed as same in decimal additions and subtractions. When we perform binary additions, there will have two outputs: Sum (S) and Carry (C) . There are four rules for binary addition.
These are given as following below:
Input A Input B Sum (S) A+B Carry(C)
0 0 0 0
0 1 1 0
1 0 1 0
1 1 0 1
There are four rules for binary subtraction. These are given as following below:
Input A Input B Subtract (S) A-B Borrow(B)
0 0 0 0
0 1 0 0
1 0 1 0
1 1 0 0
Borrow 1 is required from next higher order bit to subtract 1 from 0. So, result became 0
There are four rules for binary multiplication. These are given as following below:
Input A Input B Multiply (M) A*B
0 0 0
0 1 0
1 0 0
1 1 1
Whenever at least one input is 0, then multiplication is always 0
There are four part in any division: Dividend, Divisor, quotient, and remainder. These are given as following rules for binary division:
Input A Input B Divide (D) A/B
0 0 Not defined
0 1 0
1 0 Not defined
1 1 1
Whenever divisor is 0, then result is always not defined
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