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How to carry out basic operations on number systems?
- Adding 23 and 69
- Subtracting 53 from 126
- Subtracting 184 from 57
- Multiplying 85 * 23
For the numbers listed I need to know how to do a working of how to convert the decimal numbers into binary, how to perform the calculations in binary and converting it back into decimal again. Will appreciate any answers & am prepared to give out 5 stars for best answer
1 Answer
- ?Lv 75 years agoFavorite Answer
Base 10 to base 2.
Divide by 2 keeping remainders until quotient is zero. Read out remainders in reverse order.
2|5
2|2 1
2|1 0
_|0 1
101
base 2 to base 10.
each 1 digit corresponds to a power of 2. Add up all such powers.
101 = 2^2 + 2^0 = 4+1 = 5
addition base 2
0+1 = 1
1+0 = 1
1+1 = 10
1+1+1 = 11
do longhand
Subtraction
11 - 1 = 10
10 - 1 = 1
1 - 1 = 0
do longhand
multiplication
shift and add
do longhand
Example
__11 2+1=3
__11
------
0011
0110
-----
1001
1+0 = 1
1+1 = 10
1+carry 1 is 10
8+1 = 9
I would convert to and from base 2 using base 16 as an intermediate.
Hex digits are groups of 4 binary digits.
Older programmers might use base 8 in the same fashion. Octal digits are groups of 3 binary digits.