Number Systems

Binary and Hexadecimal

Computers operate in binary (base 2). Each digit is a 0 or 1, called a bit. In LC-3, everything is 16 bits wide.

Hexadecimal (base 16) is a convenient shorthand — each hex digit represents exactly 4 bits:

Hex

Binary

Decimal

0	0000	0
5	0101	5
A	1010	10
F	1111	15

So x3000 = 0011 0000 0000 0000 in binary = 12288 in decimal.

Two's Complement

LC-3 uses two's complement to represent signed integers. In a 16-bit system:

Positive numbers: 0000 0000 0000 0001 = 1

Negative numbers: flip all bits and add 1

-1 = 1111 1111 1111 1111 = xFFFF

Range: -32768 to 32767

To negate a number: invert all bits, then add 1.

For example, to get -5:

5 = 0000 0000 0000 0101

Invert: 1111 1111 1111 1010

Add 1: 1111 1111 1111 1011 = xFFFB