Binary

BINARY : COUNTING TO 1 Computer Sciences NRHS

Simple Math First … ONES TENS HUNDREDS THOUSANDS X 10 X 10 X 10 BASE 10 3 6 5 9

BASE 10 = TEN DIGITS 1 2 3 4 5 6 7 8 9 0

3659 = ,[object Object],[object Object],[object Object],[object Object],NOTE: Numbers are always broken down from right to left.

Binary… 1 4 8 X 2 X 2 X 2 BASE 2 2 BIT 0 0 0 0

BINARY IS LIKE A LIGHT SWITCH 0 = OFF 1 = ON

What number is this? 1 4 8 Answer: 0 2 0 0 0 0

8 Bits = 1 Byte 16 32 64 128 What is the highest possible number in one Byte? 255 8 4 2 1

What number is this? 16 32 64 128 Answer: 170 8 4 2 1 1 0 1 0 1 0 1 0

CD ROM = up to 900 MB DVD ROM = up to 4.7 GB Average MP3 = 1.5 MB

Let’s Start With ½ a Byte (aka Nibble) How do you know that this number is 13? 8 4 2 1 1 1 0 1

Determine which are “on” and which are “off” First, you ignore the numbers that are turned off. 8 4 2 1 1 1 0 1

Create the Equation Then, you add together the numbers that are turned on. + + + 8 4 2 1 1 1 0 1

Do the Equation The equation is … 8+4+1 = 13 + + + 8 4 2 1 1 1 0 1

Convert from Base10 to Binary How do you find the binary for 14? 8 4 2 1

Start with the Largest Number on the Left Ask: Does 8 go into 14? If YES … put a 1 in that box to turn it “on”. 1 8 4 2 1

Subtract to get the Remainder 14-8=6 1 8 4 2 1

Move to the next largest number Ask: Does 4 go into 6? If YES … put a 1 in that box to turn it “on”. 1 1 8 4 2 1

Subtract to get the Remainder 6-4=2 1 1 8 4 2 1

Move to the next largest number Ask: Does 2 go into 2? If YES … put a 1 in that box to turn it “on”. 1 1 1 8 4 2 1

Subtract to get the Remainder 2-2=0 1 1 1 8 4 2 1

Move to the next largest number Ask: Does 1 go into 0? If NO… put a 0 in that box to turn it “off”. 1 1 1 0 8 4 2 1

Now Let’s Do a Byte 16 32 64 128 What is the first step to find out what binary is for 235? 8 4 2 1

Start with the Largest Number on the Left 16 32 64 128 Does 128 go into 235? 235-128 = 107 YES! Turn 128 “on” 1 8 4 2 1

Move one number to the right 16 32 64 128 Does 64 go into 107? 107-64 = 43 YES! Turn 64“on” 1 1 8 4 2 1

Move one number to the right 16 32 64 128 Does 32 go into 43? 43-32= 11 YES! Turn 32“on” 1 1 1 8 4 2 1

Move one number to the right 16 32 64 128 Does 16 go into 11? 11-16= NO NO! Turn 16 “off” 1 1 1 0 8 4 2 1

Move one number to the right 16 32 64 128 Does 8 go into 11? 11-8= 3 YES! Turn 8 “on” 1 1 1 0 1 8 4 2 1

Move one number to the right 16 32 64 128 Does 4 go into 3? 3-4= NO NO! Turn 4 “off” 1 1 1 0 1 0 8 4 2 1

Move one number to the right 16 32 64 128 Does 2 go into 3? 3-2= 1 YES! Turn 2 “on” 1 1 1 0 1 0 1 8 4 2 1

Move one number to the right 16 32 64 128 Does 1 go into 1? 1-1= 0 YES! Turn 1 “on” 1 1 1 0 1 0 1 1 8 4 2 1

Move one number to the right 16 32 64 128 235 in Binary! 1 1 1 0 1 0 1 1 8 4 2 1

How do you get the number 270? ,[object Object],[object Object],[object Object],[object Object],[object Object]

Make a Table 1 32768 16384 8192 4096 2048 1024 512 256 128 64 32 16 8 4 2

Get Rid of All Numbers Larger than the One You Are Trying To Convert (they become 0s) 1 256 128 64 32 16 8 4 2 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0

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