1. © 2003, Cisco Systems, Inc. All rights reserved.

2. Basics Information

3. Objectives (Cont.) Convert a decimal number to a binary number
Convert a binary number to a decimal number
Convert a binary number to a hexadecimal number
Convert a hexadecimal number to a binary number
Lesson Aim
<Enter lesson aim here.>

4. Units of Information Units Bytes Bits bit (b) — 1 bit byte (B) 1 byte
kilobyte (KB)
1000 bytes
8000 bits
megabyte (MB)
1 million bytes
8 million bits
gigabyte (GB)
1 billion bytes
8 billion bits

5. Decimal-to-Binary Conversion
(r = remainder)
253/2 = r 1
126/2 = r 0
63/2 = r 1
31/2 = r 1
15/2 = r 1
7/2 = r 1
3/2 = r 1
1/2 = r 1
Converting a decimal number (253) to binary by successive division by 2
Write the binary number in order of the last bit first:

6. Base 2 Numbering System
Number of
Symbols 2 2 2 2 2 2 2 2
Symbols
0, 1
0, 1
0, 1
0, 1
0, 1
0, 1
0, 1
0, 1
Base Exponent 27 26 25 24 23 22 21 20
Place Value
128 64 32 16 8 4 2 1
Example:
Convert decimal
35 to binary 1 1 1

7. Binary-to-Decimal Conversion
Convert the binary number to a decimal number
(Binary bits have decimal values)
Decimal Position Value
1 or
128*1 + 64*1 + 32*1 + 16*1 + 8*1 + 4*1 + 2*0 + 1*1
= 253

8. Base 2 Number System
Number of
Symbols 2
Symbols
0, 1
Base Exponent 27 26 25 24 23 22 21 20
Place Value
128 64 32 16 8 4 2 1
Example:
Binary Number 1 1 1 1 1
Decimal number
Total: 185
128 32 16 8 1

9. Binary-and-Hexadecimal Systems 00 1 01 2 02 3 03 4 04 5 05 6 06 7 07 8 08 9 09 10 0A 11 0B 12 0C 13 0D 14 0E 15 0F 16 10 32 20 64 40
128 80
255 FF

10. Binary-and-Hexadecimal Number Systems
0000 =
1000 = 8
0001 = 1
1001 = 9
0010 = 2
1010 = A
0011 = 3
1011 = B
0100 = 4
1100 = C
0101 = 5
1101 = D
0110 = 6
1110 = E
0111 = 7
1111 = F

11. Binary-to-Hexadecimal Conversion Example
Converts to:
Converts to:
F D C
So:
Binary
= 1245F7DC9 hexadecimal

12. Hexadecimal-to-Binary Conversion Example
Converts to:
So:
2102 hexadecimal converts to: binary

13. Summary (Cont.)
Computers can recognize and process data only by using the binary numbering system. The binary number system is made up of 0s and 1s.
Decimal numbers can be converted to binary numbers by following specific procedures.
The hexadecimal number system is used frequently at higher levels of computation. The hexadecimal number system uses 16 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F.