Chapter 3: Binary and Hexadecimal Numbers

Hex > Binary 0

0000

Hex > Binary 1

0001

Hex > Binary 2

0010

Hex > Binary 3

0011

Hex > Binary 4

0100

Hex > Binary 5

0101

Hex > Binary 6

0110

Hex > Binary 7

0111

Hex > Binary E

1110

Hex > Binary F

1111

Hex > Binary 8

1000

Hex > Binary 9

1001

Hex > Binary A

1010

Hex > Binary B

1011

Hex > Binary C

1100

Hex > Binary D

1101

Binary Numbers

only 0's and 1's. The place value on the right is the 1's place, just as in decimal. The place value of each next place moving left is twice the place value of the current place, just as the next place values in decimal are ten times the current place value. To convert from binary to decimal, add up the place values of the 1-bits.

Twos Complement

take the opposite of a number, complement each bit (change a 0 to a 1 or a 1 to a 0) and then add 1 to the result.

ASCII code and Unicode

to represent a character, computers use a code like the following, where each number in memory will display as a different character. Extended ASCII had 256 characters. Unicode has at least 2 bytes, for 65,536 characters. Example: 37: % 43: +

IEEE 754 Standard

to represent floating-point numbers, most computer manufacturers use a standard representation, either 32 or 64 bits (4 or 8 bytes). The 32-bit standard follows.

Fixed-point

use some number of places after the point and some number before the point, and figure out the binary number based on those place values.