By R.S. Sedha
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Additional resources for A Textbook of Digital Electronics
Find the decimal forms for the two binary numbers: 11012 and 101112 (Gauhati: University 2007) Solution. Given: the binary number = 1101 Binary number 11012 Step 1. 1 1 0 1 Step 2. 23 22 21 20 Step 3. 23 22 21 20 Created with Print2PDF. com/ 28 A TEXTBOOK OF DIGITAL ELECTRONICS Step 4. 23 + 22 + 20 = 8+ 4+ 1 = 1310 11012 = 1310 Ans. Binary number 101112 Given: the binary number 10111 Step 1. 1 0 1 1 1 Step 2. 24 23 22 21 20 Step 3. 24 23 22 21 20 Step 4. 24 + 22 + 21 + 20 = 16 + 4 + 2 + 1 = 23 101112 = 2310 Ans.
Following is the procedure that is used for conversion: Step 1. Begin by multiplying the given decimal fraction by 2 and then multiplying each resulting fractional part of the product by 2. Step 2. Repeat step 1 until the fractional product is zero or until the desired number of decimal places is reached. Step 3. The carried bits or carries generated by the multiplication produce the binary number. The first carry produced is the most-significant bit (MSB) and the last carry is the least significant bit (LSB).
Thus a list of eight binary weights would be (read from right to left): 128, 64, 32, 16, 8, 4, 2, 1 Consider, for example, the conversion of decimal number to its binary equivalent using sum-ofweights method. Then we know that, the number 9 can be expressed as the sum of binary weights as follows: 9=8+1 or Placing 1s in the appropriate weight write the binary number for decimal 9 as: 9 = 23 + 21 positions, 23 and 20 and 0s in the 22 and 21 positions, we can 23 22 21 20 1 0 0 1 910 = 10012 Example 2-10.
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