Binary to Decimal Conversion Worksheet
Try to work out these binary numbers
The word binary means two. The binary number system has two symbols: 0 and 1. When we write binary
numbers we use a “2” for a subscript to represent the binary system.
A “bit” (short for “binary digit”) is the smallest piece of data that a computer knows. It is a single digit, which
can be a one or a zero. A “word” is a group of any number of bits. A “byte” is a group of 8 bits, You would
have 256 different combinations if you wrote down all the different possible combinations of ones and zeros that
could make up a byte.
One – on
Zero – off
Add up the place value for everyone 1.
27
128
1
0
0
0
1
1
26
64
0
0
0
1
1
1
25
32
1
1
1
1
1
1
24
16
0
1
1
0
0
0
23
8
1
0
1
0
1
0
22
4
0
0
0
0
1
0
21
2
0
1
0
1
1
0
20
1
1
0
0
0
0
1
Mathematical Way
Binary to Decimal
1
27
0
26
Find the place value for everyone. Multiple 1 by that place value.
1
25
0
24
1
23
0
22
0
21
1
20
1 x 27 1 x 25 1 x 23 1 x 20
128
+ 32 +
8 +
1
=
=
Converter Tool with explanation.
http://acc6.its.brooklyn.cuny.edu/~gurwitz/core5/nav2tool.html
Cisco Binary Game:
Practice:
Convert
1100011 to decimal
169
Answer
From Binary to Hexadecimal
Hexidecimal, or base 16, number system is a common system used with computers. It is a human-friendly
representation of binary-coded values in computing and digital electronics. It is used in web pages for colors.
Hexadecimal is represented by 16 digits 0-9 and then A – F
A = 10, B = 11, C = 12, D = 13, E = 14, F = 15
Converting Binary to Hex
10001100101001
STEP ONE: Take the binary number and from right to left, group all placeholders in groups of 4. Add
leading zeros, if necessary:
0010
0011
0010
1001
2
STEP TWO: Convert each triplet to its single-digit octal equivalent. (HINT: For each group of 4, the
hex conversion is the same as converting to a decimal number):
0010
0011
2
3
2329
0010
2
1001
2
9 hex
16
You do it: Practice: convert
11001110 to Hex
Converting Hex to Binary
2329
16
STEP ONE: Take each hex digit and convert each digit to a binary form. Keep leading zeros:
0010
2329
16
0011
0010 1001
10001100101001
=
You do it: Practice: convert
4AB to Binary
Octal - Base 8 Numbering System
The octal, or base 8, number system is a common system used with computers. Because of its relationship with
the binary system, it is useful in programming some types of computers.
Converting Binary to Octal
Take the binary number
10001100101001
STEP ONE: Take the binary number and from right to left, group all placeholders in group of 3. Add
leading zero at end if necessary:
010
001 100 101 001
2
STEP TWO: Find the binary number for that group of 3.
010
001 100 101 001
2
1
4
10001100101001 =
2
5
1
21451
oct
8
You do it: Practice: convert
11001110 to Oct
Converting Octal to Binary
43520
8
Bring the numbers the binary group of 3
4
100
3
011
5
101
2
0
010 000
You do it: Practice: convert
100011101010000
2643 to binary
=
43520 oct
Binary Numbers
The base value of a number system tells us how many digits we have to work with and what is the place value of each
digit in a number.
Binary is base 2
Consist of either 0 or 1. 0 is false or off
1 is true or on
Decimal
Binary
Base 10
Base 2
89
1011001
Hexadecimal
Octal
Base 16
Base 8
59
131
(8 x 101 ) + (9 x 100) = 89
(1 * 26) + (1 * 24) + (1 * 23) + (1 *
20) = 89
(5 * 161) + (9 * 160) = 89
(1 * 82) + (3 * 81+ (1 * 80) = 89
27
26
25
24
23
22
21
2o
128
0
64
1
32
0
16
1
8
1
4
0
2
0
1
1
To convert to decimal, multiply the
(1 * 26) )+( 1 *24) + (1 * 23 )+ (1 * 20)
64 + 16 +
8 + 1 = 89
Hexadecimal is base 16 Hex number 59 convert to decimal
163
162
161
16o
4096
256
16
5
1
9
A
2
use 0-9 for digits 0 – 9 use A-F for digits 10-15
Convert to Decimal: Multiply the digit by its base 16 value for the place value position
(5 x 161) + (9 x 160)
5 x 161 = 5 x 16 = 80
9 x 160 = 9 x 1 = 9 80 + 9 = 89
A = 10
(10 x 161) + (2 x 160) =
160 + 2 = 162
OCTAL TO DECIMAL Octal is base 8
Octal number 131 convert to decimal
83
82
81
8o
512
64
1
8
3
1
1
Convert to Decimal: Multiply the digit by its base 8 value for the place value position
(1 x 82) + ( 3 x 81) + (1 x 80)
1 x 64 = 64
3 x 81 = 3 x 8 = 24
1 x 80 = 1 x 1 = 1
64
+
24
+
1
= 89
Practice:
Convert to decimal
Numbering System
1100111 bin
3BC hex
3540 oct
Decimal