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SANTA CLARA COUNTY OFFICE OF EDUCATION
North County Regional Occupational Program (NCROP)
Engineering Technology
DECIMAL and BINARY
Computers can quickly manipulate digital ‘0’ and ‘1’, so semiconductor electronics is
based on a binary system of numbers. We must be able to convert decimal numbers (base
10) to binary (base 2).
Decimal is the base 10 counting system that we use everyday. Focusing on integer
numbers, the ones place represents 100, the tens place represents 101, the hundreds
represents 102, etc.
For example:
Decimal
371
= [(3*102) + (7*101) + (1*100)]
= 300
+
70
+
1
TO CONVERT DECIMAL TO BINARY:
1
Continually divide the dividend by ‘2’ and keep track of each remainder, whether
‘0’ or ‘1’
2
Stop when the quotient value is 0. This will be the Most Significant Bit, or MSB.
3
Write the string of remainders with the MSB on the left and the LSB on the right.
4
This series is the binary equivalent to the original decimal number.
UIP0100 – Binary Handout.doc
SANTA CLARA COUNTY OFFICE OF EDUCATION
North County Regional Occupational Program (NCROP)
Engineering Technology
DECIMAL and BINARY (cont)
Example 1: Find the binary equivalent to decimal 8.
Quotient
8
4
2
1
0
Remainder
0
0
0
1
Comment
The decimal number
Least Significant Bit (LSB)
Most Significant Bit (MSB)
Write the sequence starting from the MSB to the LSB. This would be ‘1000’,
which is the binary representation of decimal 8.
Example 2: Find the binary equivalent to decimal 23.
Quotient
23
11
5
2
1
0
Remainder
1
1
1
0
1
Comment
The decimal number
Least Significant Bit (LSB)
Most Significant Bit (MSB)
The binary equivalent of decimal 23 is ‘1 0111’
Example 3: Find the binary equivalent to decimal 217.
Quotient
217
108
54
27
13
6
3
1
0
Remainder
1
0
0
1
1
0
1
1
Comment
The decimal number
Least Significant Bit (LSB)
Most Significant Bit (MSB)
The binary equivalent of decimal 219 is ‘1101 1001’
UIP0100 – Binary Handout.doc
SANTA CLARA COUNTY OFFICE OF EDUCATION
North County Regional Occupational Program (NCROP)
Engineering Technology
DECIMAL and BINARY (cont)
TO CONVERT BINARY TO DECIMAL:
Each successive digit, starting from the LSB and incrementing to the left, represents 2n,
where ‘n’ represents the nth power of that digit.
Convert binary ‘1000’ to its decimal equivalent:
=
1
0
0
0
= [(1*23) + (0*22) + (0*21) + (0*20)]
=
8
+
0
+
0
+ 0
= decimal 8.
Convert binary ‘1100 0111’ to its decimal equivalent
=
1
1
0
0
0
1
1
1
= [(1*27) + (1*26) + (0*25) + (0*24) + (0*23) + (1*22) + (1*21) + (1*20)]
= [ 128
+ 64
+
= decimal 199
UIP0100 – Binary Handout.doc
0
+ 0
+
0
+ 4
+
2
+ 1]
SANTA CLARA COUNTY OFFICE OF EDUCATION
North County Regional Occupational Program (NCROP)
Engineering Technology
Decimal / Binary Conversion Problems
Convert the following decimal numbers to their binary equivalents. Show your work.
1) 6
2) 13
3) 38
4) 64
5) 85
6) 100
7) 123
8) 158
9) 249
10) 255
Convert the following binary number to their decimal equivalents. Show your work.
11) 0011
12) 0111
13) 1010
14) 1111
15) 0101 1101
16) 0110 1001
17) 0111 1100
18) 1010 1010
19) 1111 0111
20) 1111 1011
UIP0100 – Binary Handout.doc