Math Review Do you remember, from math class, how exponentiation operations are typically represented? anan is known as the "base" a is known as the "base" is known as the "exponent". n is known as the "exponent". You might say, " raised to the power of ". You might say, "a raised to the power of n".

Warm Up Try to find a value for each of the exponents shown below. 2 0 = 2 0 = 2 1 = 2 1 = 2 2 = 2 2 = 2 3 = 2 3 = = =

Bit Patterns Computer Number Systems Scott Baranick & Daniel Velasquez

Bits and Bytes A bit is the short name for "binary digit". A bit is the short name for "binary digit". A bit can store only two values. 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. A byte is a series of 8 bits or switches.

Bits and Bytes A kilobyte is 1024 bytes, A kilobyte is 1024 bytes, – In other words, 2 10 –This is often rounded to 1,000 bytes

Bits and Bytes A megabyte is either 1000 or 1024 kilobytes. A megabyte is either 1000 or 1024 kilobytes. A gigabyte is either 1000 or 1024 megabytes. A gigabyte is either 1000 or 1024 megabytes. What's next? What's next?

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

Decimal vs. Binary x x x x x x = = 5 10

Counting in Base

Counting in Base 2 "Computer Science Unplugged" Class Activity: "Computer Science Unplugged" Class Activity: Use Flip cards to demonstrate binary addition. Use Flip cards to demonstrate binary addition. Also use the hats to show the place values. 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. 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 x 2 0 = 1 x one = 1 0 x 2 1 = 0 x two = 0 1 x 2 2 = 1 x four = 4 0 x 2 3 = 0 x eight = 0 0 x 2 4 = 0 x sixteen = 0 1 x 2 5 = 1 x thirty-two = 32 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. 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? What does this binary number represent in base 10? Answer: 15 Answer: 15 Notice that this is the same as the base of 2 raised by the number of bits minus 1. Notice that this is the same as the base of 2 raised by the number of bits minus 1. Formula 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? So what then are the largest numbers that can be represented using 16 bits? 32 bits? and 64 bits?

Summary Recognize that computers, regardless of brand or type, are binary machines. Recognize that computers, regardless of brand or type, are binary machines. All the math done inside a computer is done in binary. 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. 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.

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