Binary Decimal Review n n n Each binary

Binary Decimal

Review n n n Each binary digit (bit) is a power of 2 Place the bits, multiply, and add Example: 110101102 . . . 27 26 25 24 23 22 21 20 . . . 128 64 32 16 8 4 2 1 . . .

Convert the following from binary to decimal 11012 = ? 0011012 = ? 101110102 = ?

Decimal Binary

Converting from Decimal to Binary 1. 2. 3. 4. 5. 6. Write out the powers of 2 Subtract the largest power of 2 that is less than your number Make note of which power of 2 you subtracted with a 1 (unused powers of 2 will be 0) Subtract the next largest power of 2 from the result that you have Repeat until you reach 0 Build your binary number from the 1 s and 0 s that you have placed

Examples 1510 = ? 4910 = ? . . . 27 26 25 24 23 22 21 20 . . . 128 64 32 16 8 4 2 1 . . .

Convert the following from decimal to binary 810 = ? 2510 = ? 8310 = ?

Data Representation n n If we have 2 bits, how many different binary numbers can we make? And if we had 3? How about 4? Umm. . . 32?

How many combinations? n n Each bit can only be a 0 or 1 (2 choices) The number of distinct combinations of n-bits is given by 2 n

Pixel Depth n n n Pixel ~ Picture element What does an image look like when we zoom in? An image is merely a matrix of numbers ¡ n n Numbers ~ Colors Number of bits restricts the number colors we can use Example: Lower your display setting’s color quality

What is the maximum value of a 16 -bit integer?