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.