CCNA math conversion tables - binary, decimal, hexadecimal

This post is dedicated to explaining CCNA math. It constitutes Issue 5 of my CCNA 200-301 study notes.

For a more comprehensive CCNA math resource: CCNA math portal.

The meaning of base 2, 10, and 16 number systems
Decimal to binary conversion
Binary to decimal conversion
Hexadecimal to decimal conversion
Decimal to hexadecimal conversion
Key references

You may also be interested in CCNA 200-301 study notes.

The meaning of base 2, 10, and 16 number systems

base-2-10-16-number-systems — The meaning of base 2, 10, and 16 number systems

*How the binary system works: 0, 1

Example 1: 10 is 1 value of 8 and 0 value of 4 and 1 value of 2 and 0 value of 1 =1010

Example 2: 9 = 1×8 + 0x4 + 0x2 + 1×1 = 1001

Example 3: 13 = 1×8 + 1×4 +0x2 +1×1 = 1101

*How the decimal system works: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Example 1: 10 is 1 value of 10 and 0 value of 1

Example 2: 14 is 1 value of 10 and 4 values of 1 = 1×10 + 4×1

Example 3: 314 = 3×100 + 1×10 + 4×1

*How the hexadecimal system works: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

Example 1: 17 = 1×16 + 1×1 = 11

Example 2: 26 = 1 value of 16 and 10 values of 1 = 1×16 + 10×1 = 1A

Example 3: 30 = 1×16 + 14×1 = 1E

ccna-math — Convert between number systems like it’s 1999 by using these conversion tables (image courtesy of Khan Academy)

Decimal to binary conversion

Example 1: convert 221 to binary.

221 – 128 = 93

Now,

93 – 64 = 29

29 – 16 = 13

13 – 8 = 5

5 – 4 = 1

1-1 = 0

2⁷	2⁶	2⁵	2⁴	2³	2²	2¹	2⁰
128	64	32	16	8	4	2	1
1	1	0	1	1	1	0	1

221 equals 11011101.

Example 2: convert the following IPv4 address to binary format.

IPv4 address: 192.168.1.254.

An IPv4 address is a series of 32 bits (4 bytes) split up into four octets then written in dotted decimal format.

We want to write each octet value in binary numbers. Following the previous examples:

Decimal	192	168	1	254
Binary	11000000	10101000	00000001	11111110

Binary to decimal conversion

Example: 10001111 equals 143. But how come?

2⁷	2⁶	2⁵	2⁴	2³	2²	2¹	2⁰
128	64	32	16	8	4	2	1
1	0	0	0	1	1	1	1

1×128 + 1×8 +1×4 +1×2 + 1×1 = 128 + 8 + 4 + 2 + 1 = 143.

Hexadecimal to decimal conversion

CDE in hexadecimal = 3294 in decimal. But how come?

16⁷	16⁶	16⁵	16⁴	16³	16²	16¹	16⁰
				4096	256	16	1
					C (12)	D (13)	E (14)

CDE = 12×256 + 13×16 + 14×1 = 3072 + 208 + 14 = 3294.

Decimal to hexadecimal conversion

Convert 3294 to hexadecimal numbers.

3294/256 = 12.867

3294 – 12×256 = 222

Now,

222/16 = 13.875

222 – 13×16 = 14

Finally,

14/1 = 14

14 – 14×1 = 0

3294 = 12×256 + 13×16 + 14×1 = CDE

Key references

Hexadecimal number system | Applying mathematical reasoning | Pre-Algebra | Khan Academy