Binary Lesson 5Binary Lesson 5CountingCounting

Powers of 2Powers of 2

One bit has 2 possible values (2^1)One bit has 2 possible values (2^1) 0 or 10 or 1

Two bits have 4 possible values (2^2)Two bits have 4 possible values (2^2) 00 01 11 1000 01 11 10

Three bits have Three bits have 8 values (2^3)8 values (2^3) 000 001 010 011 100 101 110 111000 001 010 011 100 101 110 111

Four bits have 16 values (2^4)Four bits have 16 values (2^4) 0000 0001 ... 1110 11110000 0001 ... 1110 1111

A ByteA Byte

8 bits, from 0000000 to 111111118 bits, from 0000000 to 11111111 2^8 combinations2^8 combinations 2x2x2x2x2x2x2x2 = 2562x2x2x2x2x2x2x2 = 256 In Hex, 00 to FFIn Hex, 00 to FF 16 x 16 = 25616 x 16 = 256 2^8 = 2^4 x 2^42^8 = 2^4 x 2^4

A Word – 16 BitsA Word – 16 Bits

0000 to FFFF0000 to FFFF 2^16 values = 65,5362^16 values = 65,536 2^16 = 2^8 x 2^8 = 256 x 2562^16 = 2^8 x 2^8 = 256 x 256 2^16 = 2^4 x 2^4 x 2^4 x 2^4 2^16 = 2^4 x 2^4 x 2^4 x 2^4 = 16 x 16 x 16 x 16= 16 x 16 x 16 x 16

The Easy WayThe Easy Way

2^10 = 1,024, written as 1 K2^10 = 1,024, written as 1 K So 16 bits have 2^16 valuesSo 16 bits have 2^16 values 2^16 = 2^6 x 2^10 = 2^6 K = 64 K2^16 = 2^6 x 2^10 = 2^6 K = 64 K Approximately 64,000Approximately 64,000

32 Bits32 Bits

Range of values fromRange of values from 0000:0000 to FFFF:FFFF0000:0000 to FFFF:FFFF 2^32 values2^32 values 2^2 x 2^10 x 2^10 x 2^102^2 x 2^10 x 2^10 x 2^10 4 K K K = 4 K M = 4 G4 K K K = 4 K M = 4 G Approximately 4,000,000,000Approximately 4,000,000,000

64 Bits64 Bits

0000:0000:0000:0000 to 0000:0000:0000:0000 to 1111:1111:1111:11111111:1111:1111:1111

2^642^64 2^4 x 2^10 x 2^10 x 2^10 x 2^10 x 2^10 x 2^102^4 x 2^10 x 2^10 x 2^10 x 2^10 x 2^10 x 2^10

16 K K K K K K = 16 G G16 K K K K K K = 16 G G ApproximatelyApproximately 16,000,000,000,000,000,00016,000,000,000,000,000,000

128 Bits128 Bits

The entire IPv6 address space, fromThe entire IPv6 address space, from 0000:0000:0000:0000:0000:0000:0000:00000000:0000:0000:0000:0000:0000:0000:0000 toto ffff:ffff:ffff:ffff:ffff:ffff:ffff:ffffffff:ffff:ffff:ffff:ffff:ffff:ffff:ffff 2^128 = 2^8 x 2^1202^128 = 2^8 x 2^120 2^8 x 2^30 x 2^30 x 2^30 x 2^30 2^8 x 2^30 x 2^30 x 2^30 x 2^30 256 G G G G256 G G G G ApproximatelyApproximately 256,000,000,000,000,000,000,000,000,000,000,000,000256,000,000,000,000,000,000,000,000,000,000,000,000

Slash NotationSlash Notation

fe80::/64 means 64 bits are fixed, so 64 fe80::/64 means 64 bits are fixed, so 64 bits varybits vary 2^64 addresses2^64 addresses

fe80::/16 means 16 bits are fixed, so 112 fe80::/16 means 16 bits are fixed, so 112 bits varybits vary 2^112 addresses2^112 addresses

2620:1:b::/48 means 48 bits are fixed, so 2620:1:b::/48 means 48 bits are fixed, so 80 bits vary80 bits vary 2^80 addresses2^80 addresses

Binary iClicker Binary iClicker QuestionsQuestions

How many different nybbles are How many different nybbles are there?there?

1 nybble has 4 bits1 nybble has 4 bits

A.A. 22

B.B. 44

C.C. 1616

D.D. 256256

E.E. 6553665536

How many different bytes are How many different bytes are there?there?

1 byte has 8 bits1 byte has 8 bits

A.A. 1616

B.B. 256256

C.C. 65,53665,536

D.D. 16,000,00016,000,000

E.E. 4,000,000,0004,000,000,000

How many different words are How many different words are there?there?

1 word has 16 bits1 word has 16 bitsAn approximate value is OKAn approximate value is OK

A.A. 256256

B.B. 64,00064,000

C.C. 16,000,00016,000,000

D.D. 4,000,000,0004,000,000,000

E.E. 1,000,000,000,0001,000,000,000,000

How many addresses are in this How many addresses are in this range?range?

ff02::/112ff02::/112(An approximate answer is OK)(An approximate answer is OK)

A.A. 11

B.B. 256256

C.C. 64,00064,000

D.D. 16,000,00016,000,000

E.E. 4,000,000,0004,000,000,000

How many addresses are in this How many addresses are in this range?range?ff02::/96ff02::/96

(An approximate answer is OK)(An approximate answer is OK)

A.A. 64,00064,000

B.B. 4,000,000,0004,000,000,000

C.C. 256,000,000,000,000256,000,000,000,000

D.D. 16,000,000,000,000,000,00016,000,000,000,000,000,000

E.E. 64,000,000,000,000,000,000,000,000,00064,000,000,000,000,000,000,000,000,000

How many addresses are in this How many addresses are in this range?range?

2610:1:b::/642610:1:b::/64(An approximate answer is OK)(An approximate answer is OK)

A.A. 64,00064,000

B.B. 4,000,000,0004,000,000,000

C.C. 256,000,000,000,000256,000,000,000,000

D.D. 16,000,000,000,000,000,00016,000,000,000,000,000,000

E.E. 64,000,000,000,000,000,000,000,000,00064,000,000,000,000,000,000,000,000,000

How many addresses are in this How many addresses are in this range?range?

2610:1:b::/482610:1:b::/48(An approximate answer is OK)(An approximate answer is OK)

A.A. 64,00064,000

B.B. 4,000,000,0004,000,000,000

C.C. 256,000,000,000,000256,000,000,000,000

D.D. 16,000,000,000,000,000,00016,000,000,000,000,000,000

E.E. 64,000,000,000,000,000,000,000,000,00064,000,000,000,000,000,000,000,000,000

How many /64 subnets are in a How many /64 subnets are in a /48 address allocation?/48 address allocation?

(An approximate answer is OK)(An approximate answer is OK)

A.A. 1616

B.B. 256256

C.C. 64,00064,000

D.D. 4,000,000,0004,000,000,000

E.E. 256,000,000,000,000256,000,000,000,000