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Base-n Calculations (BASE)

Use the key to enter the BASE Mode when you want to perform calculations using Base-n values.

  • (BASE)

The initial default number mode when you enter the BASE Mode is decimal, which means input and calculation results use the decimal number format. Press one of the following keys to switch number modes: (DEC) for decimal, (HEX) for hexadecimal, (BIN) for binary, or (OCT) for octal.


Example: To enter the BASE Mode, switch to the binary mode, and calculate 112 + 12

  • (BIN)
  • 111

Note

Use the following keys to input the letters A through F for hexadecimal values: (A), (B), (C), (D), (E), (F).

In addition to decimal values, calculations can be performed using binary, octal and hexadecimal values.

You can specify the default number system to be applied to all input and displayed values, and the number system for individual values as you input them.

You cannot use scientific functions in binary, octal, decimal, and hexadecimal calculations. You cannot input values that include decimal part and an exponent.

If you input a value that includes a decimal part, the unit automatically cuts off the decimal part.

Negative binary, octal, and hexadecimal values are produced by taking the two's complement.

You can use the following logical operators between values in Base-n calculations: and (logical product), or (logical sum), xor (exclusive or), xnor (exclusive nor), Not (bitwise complement), and Neg (negation).

The following are the allowable ranges for each of the available number systems.

Base-n Mode Input/Output Ranges
Binary

Positive: 0 ≦ x ≦ 0111111111

Negative: 1000000000 ≦ x ≦ 1111111111
Octal Positive: 0 ≦ x ≦ 3777777777
Negative: 4000000000 ≦ x ≦ 7777777777
Decimal -2147483648 ≦ x ≦ 2147483647
Hexadecimal Positive: 0 ≦ x ≦ 7FFFFFFF
Negative: 80000000 ≦ x ≦ FFFFFFFF

Specifying the Number Mode of a Particular Input Value

You can input a special command immediately following a value to specify the number mode of that value. The special commands are: d (decimal), h (hexadecimal), b (binary), and o (octal).


Example: To calculate 1010 + 1016 + 102 + 108 and display the result as a decimal value

  • (DEC)(LOGIC)(LOGIC)(LOGIC)(d) 10
    (DEC)(LOGIC)(LOGIC)(LOGIC)(h) 10
    (DEC)(LOGIC)(LOGIC)(LOGIC)(b) 10
    (DEC)(LOGIC)(LOGIC)(LOGIC)(o) 10

  • 36

Converting a Calculation Result to another Type of Value

You can use any one of the following key operations to convert the currently displayed calculation result to another type of value: (DEC) (decimal), (HEX) (hexadecimal), (BIN) (binary), (OCT) (octal).


Example: To calculate 1510 × 310 in the decimal mode, and then convert the result to hexadecimal, binary, and octal

  • (DEC) 153
  • 45
  • (HEX)
  • 2d
  • (BIN)
  • 101101
  • (OCT)
  • 55

Note

You may not be able to convert a value from a number system whose calculation range is greater than the calculation range of the resulting number system.

The message "Math ERROR" indicates that the result has too many digits (overflow).

Base-n Calculation Examples

Example 1: To calculate 101112 + 110102 in binary (1100012)

  • (BIN) 1011111010
  • 110001

Example 2: To calculate 78 + 18 in octal (108)

  • (OCT) 71
  • 10

Example 3: To calculate 1F16 + 116 in hexadecimal (2016)

  • (HEX) 1(F)1
  • 20

Example 4: To convert the decimal value 3010 to binary, octal, and hexadecimal

  • (DEC) 30
  • 30
  • (BIN)
  • 11110
  • (OCT)
  • 36
  • (HEX)
  • 1E

Example 5: To transform the result of 510 + 516 to binary

  • (BIN) (LOGIC)(LOGIC)(LOGIC)(d) 5
    (LOGIC)(LOGIC)(LOGIC)(h) 5
  • 1010

Logical and Negation Operations

Your calculator provides you with logical operators (And, Or, Xor, Xnor) and functions (Not, Neg) for logical and negation operations on binary values. Use the menu that appears when you press(LOGIC) to input these logical operators and functions.


Note

In the case of a negative binary, octal or hexadecimal value, the calculator converts the value to binary, takes the two's complement, and then converts back to the original number base. For decimal values, the calculator merely adds a minus sign.

Examples

All of the examples below are performed in the binary mode.


Example 1: To determine the logical AND of 10102 and 11002 (10102 and 11002)

  • 1010(LOGIC)(And) 1100
  • 1000

Example 2: To determine the logical OR of 10112 and 110102 (10112 or 110102)

  • 1011(LOGIC)(Or) 11010
  • 11011

Example 3: To determine the logical XOR of 10102 and 11002 (10102 xor 11002)

  • 1010(LOGIC)(LOGIC)(Xor) 1100
  • 110

Example 4: To determine the logical XNOR of 11112 and 1012 (11112 xnor 1012)

  • 1111(LOGIC)(Xnor) 101
  • 1111110101

Example 5: To determine the bitwise complement of 10102 (Not(10102))

  • (LOGIC)(LOGIC)(Not) 1010
  • 1111110101

Example 6: To negate (take the two's complement) of 1011012 (Neg(1011012))

  • (LOGIC)(LOGIC)(Neg) 101101
  • 1111010011
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