10. Converting a number of Another Base
to Decimal Number System
Example :
(3450)8 = ?10
(3450)8 = 3 x 8^3 + 4 x 8^2 + 5 x 8^1 + 0 x 8^0
= 3 x 512 + 4 x 64 + 5 x 8 + 0 x 1
= 1536 + 256 + 40 +0
= (1832)10
Common
values
multiplied by
the
corresponding
digits
20. Binary Addition
It is the key for binary subtraction, division, multiplication.
In fourth case, a binary addition is creating a sum of (1 + 1 = 10) i.e. 0 is written
in the given column and a carry of 1 over to the next column
Case A + B Sum Carry
1 0 + 0 0 0
2 0 + 1 1 0
3 1 + 0 1 0
4 1 + 1 0 1
22. Binary Subtraction
Subtraction and Borrow, these two words will be used very frequently for the
binary subtraction.
There are four rules of binary subtraction.
In fourth case, we see that 0 – 1 creates an ambiguity. We consider this as a
borrow case and borrow 1 from the immediate left bit. Thus, this becomes 10
(decimal 2). Thus, 2-1 gives 1.
Case A - B Subtract Borrow
1 0 – 0 0 0
2 1 – 0 1 0
3 1 – 1 0 0
4 0 – 1 0 1
24. Binary Multiplication
It Binary multiplication is similar to decimal multiplication.
It is simpler than decimal multiplication because only 0s and 1s are involved.
There are four rules of binary multiplication.
Case A x B Product
1 0 x 0 0
2 0 x 1 0
3 1 x 0 0
4 1 x 1 1
26. Binary Division
Under binary division, we perform two main functions – multiplication and
subtraction.
We also call this method as the long division method.
Rules of Binary Division:
Case A ÷ B Result
1 0 ÷ 0 Divide by zero error
2 0 ÷ 1 0
3 1 ÷ 0 Divide by zero error
4 1 ÷ 1 1