Step 3 sum the products calculated in step 2 the

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Unformatted text preview: digit and the base of the number system). Step 2: Multiply the obtained column values (in Step 1) by the digits in the corresponding columns. Step 3: Sum the products calculated in Step 2. The total is the equivalent value in decimal. Example 3.1. 11OO12 = ?IO Example 3.2. 47068 = ?,o Solution: Solution: Step 1: Determine column values Column Number (from Column Value right) 1 2345 Step 1: Determine Column Number (from right) Column Value 2° = 2X- = 1 = 2 = 4 = 1 22 = 23 = 8 = 16 234 4 2= Step 2: Multiply column values by corresponding column digits 16 8 4 2 1 xl xl xO xO xl 16 8 0 0 1 Step 3: Sum the products 16 + 8 + 0 + 0+1 =25 Hence, 110012 = 2510 Step 2: Multiply column values by corresponding column digits 512 64 8 1 x4 x7 xO x6 2048 448 0 6 Step 3: Sum the products 2048 + 448 + 0 + 6 = 2502 Hence, 47068 = 250210 Solution: 1AC16 = 1 x 162 + A x 161 + C x 16° = 1x256+10x16+12x1 = 256+ 160+ 12 = 42810 Example 3.4. 40527 = ?, Solution: 40527 = 4x73 + 0x72 + 5x7' + 2x7° = 4x 343+ 0x 49+ 5x7 + 2x1 = 1372 + 0 + 35+2 = 140910 Column values 8° = 82 = = 1 = 8 83 = = 64 = 512 Example 3.5. 40526 = ?10 Solution: 40526 = 4x63 + 0x62 + 5x61 + 2x6° = 4x216 + 0x36 + 5x6 + 2x1 = 864 + 0 + 30 + 2 = 896,0 . Comparing this result with the result obtained in Example 3.4, we find that although the digits (4052) are same for both the numbers, but their decimal equivalent is different. This is because of the fact that the number in Example 3.4 is represented in base 7 number system whereas the number in Example 3.5 is represented in base 6 number system. Example 3.6. 110014 = ?10 Solution: Solution: 110014 =lx44+lx43 + Ox42 + Ox41 + 1x4° = 1 x 256 + 1 x 64 + 0x16 + 0x4 + lxl = 256 + 64 + 0 + 0+1 = 32110 Compare the result with Example 3.1. Example 3.7. IAC13 = ?10 IAC13= 1 x 132 + A x 131 + C x 13U = 1 x 169+ 10x13 + 12 x 1 = 31110 Compare the result with Example 3.3. Converting from Decimal to Another Base (Division-Remainder Technique) The following four steps are used to convert a number from decimal to another base: Step 1: Divide the decimal number to be converted by t...
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