Math Review Do you remember, from math class, how exponentiation operations are typically represented? an a is known as the "base" n is known as the "exponent". You might say, "a raised to the power of n". Define bit as a contraction of "binary digit" Talk about light switches and demonstrate

Warm Up Try to find a value for each of the exponents shown below. 20 = 21 = 22 = 23 = 24 + 21 = Mention how anything raised to the power of 0 is equal to 1.

Computer Number Systems Scott Baranick & Daniel Velasquez Bit Patterns Computer Number Systems Scott Baranick & Daniel Velasquez

Bits and Bytes A bit is the short name for "binary digit". A bit can store only two values. Off or On switch 0 or 1 False or True A byte is a series of 8 bits or switches. Define bit as a contraction of "binary digit" Talk about light switches and demonstrate the number of unique possibilities that are available if you only have 2 switches. Use the lights in your classroom to demonstrate.

Bits and Bytes A kilobyte is 1024 bytes, In other words, 210 This is often rounded to 1,000 bytes Which is 2 raised to the 10th power.

Bits and Bytes A megabyte is either 1000 or 1024 kilobytes. A gigabyte is either 1000 or 1024 megabytes. What's next? This depends on the context. Hard rives are advertised to be a certain size. They typically use 1000 since this makes the hard drive look bigger then it actually is. Ask the students if they know what the next size is. It is a terabyte. Then it is a exabyte

Number System Definitions Binary is just another name for base 2. Decimal is just another name for base 10. Hexadecimal is just another name for base 16.

Decimal vs. Binary 1 0 1 1 0 12 1 x 102 0 x 101 1 x 100 + + = 10110 You might mention here how the subscripted numbers in this slide are used to identify which base is being used to represent each overall value. = 510 + +

Counting in Base 10 0 + 1 1 + 1 2 + 1 3 . . 9 + 1 10 You might note here that, since we have no single digit to represent ten in base ten, we must use 2 digits: a 1 followed by a 0.

Counting in Base 2 "Computer Science Unplugged" Class Activity: Use Flip cards to demonstrate binary addition. Also use the hats to show the place values.

Binary Numbers Worksheet Now that we know how to count in base 2, fill in the missing binary numbers in the middle column of the worksheet.

Binary to Decimal 1 0 0 1 0 1 1 x 20 = 1 x one = 1 1 0 0 1 0 1 1 x 20 = 1 x one = 1 0 x 21 = 0 x two = 0 1 x 22 = 1 x four = 4 0 x 23 = 0 x eight = 0 0 x 24 = 0 x sixteen = 0 1 x 25 = 1 x thirty-two = 32 Step through this example on the board. 37

Back of the Worksheet Complete the top half of the back of the worksheet to demonstrate your understanding of how binary and decimal numbers relate to each other.

1111 What does this binary number represent in base 10? Answer: 15 Notice that this is the same as the base of 2 raised by the number of bits minus 1. Formula largest number = 2(n) – 1 where n represents the number of bits that are available. So what then are the largest numbers that can be represented using 16 bits? 32 bits? and 64 bits? For the homework question, I use bit sizes typical of processors available today and in the past. You may also note that the bit sizes are themselves powers of 2.

Summary Recognize that computers, regardless of brand or type, are binary machines. All the math done inside a computer is done in binary. The computer converts the numbers into decimal only when it has to display the number on the screen or show the number on a printed report.

End Day 1