Understanding Binary Basics Constructing Network Addresses Understanding Binary Basics © 2004 Cisco Systems, Inc. All rights reserved. INTRO v2.0—5-1

Outline Overview Decimal and Binary Systems Powers of 2 Basics Decimal to Binary Conversion Binary to Decimal Conversion Summary

Decimal vs. Binary Numbers Lesson Aim <Enter lesson aim here.>

Decimal and Binary Numbers Chart

Powers of 2 2 to the 0 power (20) is 1 2 to the first power (21) is 2 multiplied together 1 time. 2 2 to the second power (22) is 2 multiplied together 2 times. 2x2=4 2 to the third power (23) is 2 multiplied together 3 times. 2x2x2=8 2 to the fourth power (24) is 2 multiplied together 4 times. 2x2x2x2=16 2 to the fifth power (25) is 2 multiplied together 5 times. 2x2x2x2x2=32 2 to the sixth power (26) is 2 multiplied together 6 times. 2x2x2x2x2x2=64 2 to the seventh power (27) is 2 multiplied together 7 times. 2x2x2x2x2x2x2=128 These computations are enough to cover an 8-bit binary number. These totals will appear repeatedly in tables used for conversion. Binary (Base-2) system is the foundation of computer operations. Lesson Aim <Enter lesson aim here.>

Binary-to-Decimal Conversion

Decimal-to-Binary Conversion

Binary-to-Decimal Conversion

Summary All computers operate using a binary system. Binary systems (base 2) use only the numerals 0 and 1. Decimal systems (base 10) use the numerals 0 through 9. IP addresses are 32-bit binary numbers divided into 4 sets of 8 bits, called octets.(11111111.11111111.00000000.00000000) Using the powers of 2, a binary number can be converted into a decimal number.(255.255.0.0 Using the powers of 2, a decimal number can be converted into a binary number. 192.168.30.15=11000000.10101000.00111100.00001111 IP version 4(IPv4) address consist of 32 binary bits