ROM
CPUCMOS
HARD DRIVE RAM
RAM
POWER
onon on onoff off off off
1 bit8 bits = 1 byte
POWER
RAM
onon on onoff off off off1 1 1 10 0 0 0
1 1 1 10 0 0 0
Binary Numbers!
294,901,632$ .00Decimal System: How we express numbers
Base Ten 2 ones3 tens
6 hundreds
1 thousands0 ten thousands
9 hundred thousands4 millions
9 ten millions2 hundred million
294,901,632
100,000,000100,000,000 10,000,00010,000,000 1,000,0001,000,000 100,000100,000 10,00010,000 1,0001,000 100100 1010 11
22 99 44 99 00 11 66 33 22
294,901,632
294,901,632
100,000,000 * 2 200,000,00010,000,000 * 9 90,000,000
1,000,000 * 4 4,000,000
100,000 * 9 900,000
10,000 * 0 0
1,000 * 1 1,000100 *6 600
10*3 30
1*2 2
Binary Numbers – same concept, base two
Decimal Numbers – base ten 100,000,000100,000,000 10,000,00010,000,000 1,000,0001,000,000 100,000100,000 10,00010,000 1,0001,000 100100 1010 11
10*10*10,000,00010,000,000
10*10*1,000,0001,000,000
10*100,00010*100,000 10*10,00010*10,000 10* 1,00010* 1,000 10*10010*100 10*1010*10 10* 110* 1 11
256256 128128 6464 3232 1616 88 44 22 11
2*1282*128 2*642*64 2*322*32 2*162*16 2*82*8 2*42*4 2*22*2 2*12*1 11
128128 6464 3232 1616 88 44 22 11
00 11 =1=1
11 00 =2=2
11 11 =3=3
11 00 00 =4=4
11 00 11 =5=5
11 11 00 =6=6
11 11 11 =7=7
11 00 00 00 =8=8
11 00 00 11 =9=9
256256 128128 6464 3232 1616 88 44 22 11
2*1282*128 2*642*64 2*322*32 2*162*16 2*82*8 2*42*4 2*22*2 2*12*1 11
0 1 1 1 0 0 1 0
6464 3232 1616 88 44 22 11
11 11 11 00 00 11 00
1 twos0 ones
0 fours
0 eights
1 sixteen1 thirty-two
1 sixty-four
64 Plus 32 Plus 16 Plus 2 = 114
CPTRoom: 1 1 1 1 1 0 1 1 1
- 0 0 0 0 0 0 1 1
128128 6464 3232 1616 88 44 22 11
00 11 11 11 00 00 11 00
128 * 0 064 *1 64
32 *1 32
16 * 1 16
8 * 0 0
4 * 0 02 * 1 2
1 *0 0
0 1 1 1 0 0 1 0
114
128128 6464 3232 1616 88 44 22 11
11 00 00 00 11 11 11 11
143
00 00 00 00 11 11 11 11
11 00 00 00 00 00 11 00
00 00 11 00 00 11 00 11
11 11 11 11 11 11 11 11
15
130
37
255
+ 1 is what?
00 00 00 00 00 00 001
There are only 10 (base2) types of people in the world: those who understand binaryand those who don’t.
Decimal to Binary: What is the largest power of two that will go into our number?
128128 6464 3232 1616 88 44 22 11
no no no no no yes
5 -4 = 1
no yes
11 00 11
128128 6464 3232 1616 88 44 22 11
no no no noyes yes yes yes
114-64 = 50 50-32 = 18 18-16 = 2 2-2 = 0
6464 3232 1616 88 44 22 11
11 11 11 00 00 11 00
64 + 32 + 16 + 2 = 114
19
Decimal to Binary: What is the largest power of two that will go into our number?
128128 6464 3232 1616 88 44 22 11
128128 6464 3232 1616 88 44 22 1146
178128128 6464 3232 1616 88 44 22 11
204128128 6464 3232 1616 88 44 22 11
11 00 00 11 11
11 00 11 11 11 00
11 00 11 11 00 00 11 00
11 11 00 00 11 11 00 00
Binary Addition: 0 plus 0 = 0, 1 plus 0 = 1, 1 plus 1 = 10 (two)
1 0+ 1 0
1 0 0
1 1 1 0+ 1 0 1 0
128128 6464 3232 1616 88 44 22 11
1 1 0 0 0
1 0 1 1 1 1+ 1 0 0 1 1
Binary Addition
1 1 1 1 0 0+ 1 1 1 1 0 1
1 1 1+ 1 0 1
1 1 0 0
1 0 0 0 0 1 0
1 1 1 1 0 0 1
Remember: 1 + 0 = 1. 1 + 1 = 10. 0 + 0 = 0. 1 + 1 + 1 = 11