Page 22 - Handout Digital Electronics

Example 2

Convert 13210 to binary equivalent

Thus, the binary equivalent of 13210 is 100001002

1.8 Method 2: Using the Binary Exponential Placeholders.

This method uses the binary weighting system and is also sometimes referred to as the 8:4:2:1
approach. Each column represents a power of 2. To make things easy one must know the binary
exponential holders.

Example 1

Convert 1110 to its binary equivalent.

3
The highest power of two numbers nearest to eleven is 3, so 2 is 8

We write 8 4 2 1
1 0 1 1

We ask ourselves the question, can 8 be subtracted from 11? The answer is yes; we write one under
column. We subtract 8 from 11 and the answer is 3. The next highest power of two is 4. Ask ourselves
the question; can 4 be subtracted from 3? Answer is no. Write a zero (o) under column 4. The next
highest power of 2 is two. Ask ourselves the question, can two be subtracted from 3. The answer is yes,
and we write 1 under column 2. We subtract 2 from 3. The answer is 1. The next highest power of two is
1. We ask ourselves the question; can 1 be subtracted from 1? The answer is yes; we write a 1under
column 1.

So, 1110 is equivalent to 10112

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