# General

Q4 Is there anything I need to remember when performing BASE-N and logical operations?
A4
Yes. In addition to decimal values,calculations can be performed using binary, octal and hexadecimal values. Calculation results in the BASE-N Mode are always displayed using the currently selected number system. You can change the number system setting to change a value to another number system. You can also perform negative value calculations and logical operations.

Note:
When inputting hexadecimal values, use the keys marked with red or green alphabetic letters to input A, B, C, D, E, and F. In this case, you do not need to press the [ALPHA] key before pressing the letter key.

Converting from BASE-N to Decimal
 Number system Base example (Decimal number 28) Result Binary 2 1x 24 + 1x 23 + 1x 22 + 0x 21 + 0x20 11100 Octal 8 3x 81 + 4x 80 34 Decimal 10 2x 101 + 8x 100 28 Hexadecimal 16 1x 161 + 12x 160 1C

The following are calculations using the fx-991MS. Operation on other scientific calculator models (fx-115MS, fx-115WA, fx-991WA, fx-3650P, etc.) is similar.

Example: To convert the decimal value 28 to its binary equivalent.
1.In the BASE Mode, specify decimal as the default number base setting.
[MODE]  [MODE]  [3](BASE)  [X2](Dec)
2.Input the decimal value 28.
[2]  [8]  [=]
3. Specify binary as the desired number base.
[log](BIN)
Displayed Result: 11100

Logical operations
Logical operations display the results of the bitwise logical product (and), logical sum (or), exclusive logical sum (Xor,Exor), and exclusive negative logical sum (Xnor). In the case of negative binary, octal, and decimal values, the two's complement of the binary equivalent of the value is taken and then result is returned to its original number base value. With the decimal number base, negative values are displayed with a minus sign.

Truth Table
 A B A And B A Or B A Nand B A Nor B A Xor B 0 0 0 0 1 1 0 0 1 0 1 1 0 1 1 0 0 1 1 0 1 1 1 1 1 0 0 0

A Nand B is equivalent to: Not (A and B)
A Nor B is equivalent to: Not (A or B)
A Xor B is equivalent to : (A Or B) And (Not(A)Or Not(B))

Examples:
To take the bitwise Or and Xor of the hexadecimal values 19 and 1A, and convert the results to binary values.
Or Operation:  19 Or 1A
1.In the BASE Mode, specify hexadecimal as the default number base setting.
[MODE] [MODE]  [3](BASE)  [^](Hex)
2. Input the hexadecimal value 19.
[1]  [9]
3. Input the logical operator.
[x -1](LOGIC)  [2](or)
4. Input the hexadecimal value 1A, which will display the hexadecimal result.
[1]  [( - )](A)  [=]
Displayed Result: 1b
5. Specify binary as the desired number base.
[log](BIN)
Displayed Result: 11011

Xor Operation:  19 Xor 1A
1.In the BASE Mode, specify hexadecimal as the default number base setting.
[MODE] [MODE]  [3](BASE)  [^](Hex)
2. Input the hexadecimal value 19.
[1]  [9]
3. Input the logical operator.
[x -1](LOGIC)  [x -1](LOGIC)  [1](xor)
4. Input the hexadecimal value 1A, which will display the hexadecimal result.
[1]  [( - )](A)  [=]
Displayed Result: 3
5. Specify binary as the desired number base.
[log](BIN)
Displayed Result: 11