Math Review Do you remember from math class

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".

Warm Up Try to find a value for each of the exponents shown below. n 20 = n 21 = n 22 = n 23 = n 24 + 21 =

Bit Patterns Computer Number Systems Scott Baranick & Daniel Velasquez

Bits and Bytes n A bit is the short name for "binary digit". n A bit can store only two values. Off or On switch 0 or 1 False or True n A byte is a series of 8 bits or switches.

Bits and Bytes n. A kilobyte is 1024 bytes, – In other words, 210 –This is often rounded to 1, 000 bytes

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

Number System Definitions n n n 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 101 1 x 102 + 0 x 101 + 1 x 100 = 10110 1 0 12 1 x 22 + 0 x 21 + 1 x 20 = 510

Counting in Base 10 0 + 1 1 + 1 2 + 1 3. . 9 + 1 10

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

Binary Numbers Worksheet n 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 1 x 20 = 1 x one 0 x 21 = 0 x two 1 x 22 = 1 x four = = = 1 0 4 0 x 23 = 0 x eight 0 x 24 = 0 x sixteen = = 0 0 1 x 25 = 1 x thirty-two = 32 37

Back of the Worksheet n 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 n n 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. n 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. n All the math done inside a computer is done in binary. n 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. n

End Day 1