Behind the scenes in your computer Bits and Bytes Behind the scenes in your computer

All computer storage is organized into bytes Think of each byte as a little storage bin Each byte is made up of 8 bits Each bit is an electronic circuit that is either on or off (off = 0, on = 1) A specific sequence of 0’s and 1’s in a byte is called a bit pattern

So, how many bytes are in your computer? Common Prefixes Kilo 103 1,000 Thousand Mega 106 1,000,000 Million Giga 109 1,000,000,000 Billion Tera 1012 1,000,000,000,000 Trillion Typical Capacities: RAM: 1, 2, 4, 6 or 8 GB Diskette: 1.44 MB Flash drive: 2, 4, 8, 16, 32, 64, 128 GB CD: 800 MB DVD: 4.7 GB Hard Drive: 500 GB – 2 TB

Converting Between Units To Convert … From To Action KB Bytes Multiply by 1,000 (move decimal point 3 places right) MB Multiply by 1,000,000 (move decimal point 6 places right) GB Multiply by 1,000,000,000 (move decimal point 9 places right) Divide by 1,000 (move decimal point 3 places left) Divide by 1,000,000 (move decimal point 6 places left) Divide by 1,000,000,000 (move decimal point 9 places left) Example 1: 5200 KB = ? MB 5200 × 1000 = 5,200,000 bytes 5,200,000 /1,000,000 = 5.2 MB Example 2: 7.5 GB = ? KB 7.5 × 1,000,000,000 = 7,500,000,000 bytes 7,500,000,000 / 1000 = 7,500,000 KB

You Try: 3.2 MB = ? Bytes 6.4 GB = ? MB 57,000 Bytes = ? KB 25,000 KB = ? MB

What kinds of information do you store on your computer? numerical values (binary number system) text/character data (ASCII or Unicode) program instructions (machine language) images (jpg, gif, tiff, bmp, wmf, etc.) video (mp4, mov, avi, wmv, etc.) music (mp3, wav, wma, au, etc.)

“Kathy Ames” is text It would be stored like this using ASCII codes 01001011 01100001 01110100 01101000 01111001 00100000 00100001 01101101 01100101 01010011 It would be stored like this using ASCII codes

Numerical values needed for arithmetic are stored using a different scheme The numerical value 40 would be stored like this using the binary number system. 00101000 (note that “bit” stands for “binary digit”)

How do binary numbers work? Decimal Number System Binary Number System Base 10 Base 2 10 digits (0,1,2,3,4,5,6,7,8,9) 2 digits (0,1) Positional values based on powers of 10 Positional values based on powers of 2 Positional Values 128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20 Binary Number 8-bit binary number

Converting from Binary to Decimal What is the decimal value of the bit pattern 01101010 ? Positional Values 128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20 Binary Number Simple! Just add up the positional values where the 1’s appear: 64 + 32 + 8 + 2 = 106 So, we say that 011010102 = 106 decimal

Converting from Decimal to Binary How can we represent the decimal value 151 in binary? Positional Values 128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20 Binary Number Simple! Just think about money and consider positional values as bills and 151 “dollars” as the amount we must make. Then “count change” from largest “denomination” to smallest until total value of change is accumulated.

Converting from Decimal to Binary How can we represent the decimal value 151 in binary? Positional Values 128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20 Binary Number Running Total: 128

Converting from Decimal to Binary How can we represent the decimal value 151 in binary? Positional Values 128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20 Binary Number Running Total: 128

Converting from Decimal to Binary How can we represent the decimal value 151 in binary? Positional Values 128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20 Binary Number Running Total: 128

Converting from Decimal to Binary How can we represent the decimal value 151 in binary? Positional Values 128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20 Binary Number Running Total: 128 + 16 = 144

Converting from Decimal to Binary How can we represent the decimal value 151 in binary? Positional Values 128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20 Binary Number Running Total: 128 + 16 = 144

Converting from Decimal to Binary How can we represent the decimal value 151 in binary? Positional Values 128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20 Binary Number Running Total: 128 + 16 + 4 = 148

Converting from Decimal to Binary How can we represent the decimal value 151 in binary? Positional Values 128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20 Binary Number Running Total: 128 + 16 + 4 + 2 = 150

Converting from Decimal to Binary How can we represent the decimal value 151 in binary? Positional Values 128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20 Binary Number Running Total: 128 + 16 + 4 + 2 + 1 = 151 So, 151 decimal = 100101112

So What is Hexadecimal? (often called “hex”) A base 16 number system 16 possible digits: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F Positional values are powers of 16 Mainly used is as “short hand” for binary 1 hex digit = 4 binary digits

Hex Digits Dec Value 1 2 3 4 5 6 7 Hex Digit 4-bit binary 0000 0001 1 2 3 4 5 6 7 Hex Digit 4-bit binary 0000 0001 0010 0011 0100 0101 0110 0111 Dec Value 8 9 10 11 12 13 14 15 Hex Digit A B C D E F 4-bit binary 1000 1001 1010 1011 1100 1101 1110 1111

Converting from Hex to Decimal What is the decimal value of hex 3B? Positional Values 16 1 161 160 Hex Number 3 B Simple! 3 × 16 + B × 1 = 3 × 16 + 11 × 1 = 48 + 11 = 59 So, we say that 3B hex = 59 decimal

Converting from Hex to Decimal What is the decimal value of hex E4? Positional Values 16 1 161 160 Hex Number E 4 Simple! E × 16 + 4 × 1 = 14 × 16 + 4 × 1 = 224 + 4 = 228 So, we say that E4 hex = 228 decimal

Let’s take another look at Hex 3B Dec Value 1 2 3 4 5 6 7 Hex Digit 4-bit binary 0000 0001 0010 0011 0100 0101 0110 0111 Dec Value 8 9 10 11 12 13 14 15 Hex Digit A B C D E F 4-bit binary 1000 1001 1010 1011 1100 1101 1110 1111 So Hex 3B = 00111011 Binary First Digit Second Digit 3 B 0011 1011 (And note that 00111011 Binary = 32 + 16 + 8 + 2 + 1 = 59 Decimal)

Let’s take another look at Hex E4 Dec Value 1 2 3 4 5 6 7 Hex Digit 4-bit binary 0000 0001 0010 0011 0100 0101 0110 0111 Dec Value 8 9 10 11 12 13 14 15 Hex Digit A B C D E F 4-bit binary 1000 1001 1010 1011 1100 1101 1110 1111 So Hex E4 = 11100100 Binary First Digit Second Digit E 4 1110 0100 (And note that 11100100 Binary = 128 + 64 + 32 + 4 = 228 Decimal)

What about converting Binary 10100010 to Hex? Dec Value 1 2 3 4 5 6 7 Hex Digit 4-bit binary 0000 0001 0010 0011 0100 0101 0110 0111 Dec Value 8 9 10 11 12 13 14 15 Hex Digit A B C D E F 4-bit binary 1000 1001 1010 1011 1100 1101 1110 1111 First Digit Second Digit 1010 0010

What about converting Binary 10100010 to Hex? Dec Value 1 2 3 4 5 6 7 Hex Digit 4-bit binary 0000 0001 0010 0011 0100 0101 0110 0111 Dec Value 8 9 10 11 12 13 14 15 Hex Digit A B C D E F 4-bit binary 1000 1001 1010 1011 1100 1101 1110 1111 First Digit Second Digit 1010 0010 A 2 So 10100010 Binary = A2 Hex

Verify that Binary 10100010 and Hex A2 have the same Decimal values Binary 10100010 = 128 + 32 + 2 = 162 Hex A2 = A × 16 + 2 × 1 = 10 × 16 + 2 × 1 = 160 + 2 = 162

You try: Convert 210 Decimal to: Binary: Hex: Convert 2D Hex to: Decimal: Convert 10001100 Binary to: