Number bases and logic

12.1The BASE menu#

Open BASE with shift 4. HEX, DEC, OCT and BIN switch the base used to type and show numbers. The annunciator shows HEX, OCT or BIN. In another base, numbers are 36-bit integers and are shown without a decimal part. Leaving the BASE menu with EXIT returns the calculator to decimal.

12.2Convert a number to another base#

Example 12.1

255 in hexadecimal

1. Type 255 in decimal, then press HEX (second key).

   255ENTER⇧BASE41/x

Example 12.2

255 in octal

1. Press OCT (fourth key).

   255⇧BASE4LOG

Example 12.3

255 in binary

1. Press BIN (fifth key).

   255⇧BASE4LN

Example 12.4

Hexadecimal digits back to decimal

1. Choose HEX, open A…F (first key) and press F twice (sixth key), leave that menu, then press DEC (third key).

   ⇧BASE41/xΣ+XEQXEQEXIT√x

12.3Type and calculate in a base#

Choose the base first, then type digits. Arithmetic works on integers; results are cut to whole numbers.

Example 12.5

Add in hexadecimal

1. Choose HEX, type 15, ENTER, type 1 and add. 0x15 + 1 = 0x16.

   ⇧BASE41/x15ENTER1+

Example 12.6

Multiply in hexadecimal

1. 0x15 times 2 is 0x2A.

   ⇧BASE41/x15ENTER2×

12.4AND, OR, XOR, NOT, bit test and rotate#

The LOGIC menu (sixth key of BASE) has AND, OR, XOR, NOT, BIT? and ROTXY. Logic works on the 36-bit two's complement form of the numbers.

Example 12.7

12 AND 10

$$1100_2\ \text{AND}\ 1010_2=1000_2$$

1. Type 12, ENTER, 10, open BASE, LOGIC, AND (first key).

   12ENTER10⇧BASE4XEQΣ+

Example 12.8

12 OR 10

1. OR is the second key.

   12ENTER10⇧BASE4XEQ1/x

Example 12.9

12 XOR 10

1. XOR is the third key.

   12ENTER10⇧BASE4XEQ√x

Example 12.10

NOT 5

1. NOT flips every bit: 5 becomes −6.

   5⇧BASE4XEQLOG

Example 12.11

Test bit 2 of 5

1. Y = 5, X = bit number 2. BIT? (fifth key) answers Yes or No.

   5ENTER2⇧BASE4XEQLN

Example 12.12

Rotate right

1. ROTXY rotates Y right by X bits: 1 rotated by 4 gives 2^32.

   1ENTER4⇧BASE4XEQXEQ