(4) Conversion of Binary to Decimal. The converted answer can be read directly from Figure 1-

4 by looking for the most significant digit (MSD) of the binary coefficients. Thus, binary 1 (the MSD) is

found in digit position 5 which equals 16 in the decimal system. The next binary 1 is found in digit

position 4 and is worth 8 in the decimal system. The remaining binary 1 is found in position 1, and is

equal to 1. When the decimal values are added, the total is 2510.

(5) Table Construction. To construct a conversion table, the values and radix of the system must

be known. The value range determines the number of digit positions. The radix determines the base of

the number and to what power the number must be raised. In the construction of the binary table (Figure

1-4), the power of 2 is used because 2 is the radix of the binary system. The conversions you will need to

make are nearly always to the decimal system. Figure 1-4 is a conversion table that can be used for

binary-to-decimal or decimal-to-binary conversion.

(6) Conversion by Division. Using tables can be a tedious and laborious method for converting

numbers. A better method, especially for larger numbers, is division. The decimal number is repeatedly

divided by 2, and the remainder after each division is used to indicate the coefficients of the binary

number to be formed. Note that the binary number derived is written from the bottom up. Here are some

examples that show how to use the division method in converting from decimal to binary.

(a) Example 1:

(1) Convert 12510 to the binary system.

125 / 2 = 62 + remainder of 1

62 / 2 = 31 + remainder of 0

31 /2 = 15 + remainder of 1

15 /2 =7 + remainder of 1

7 /2 =3 + remainder of 1

3 / 2 = 1 + remainder of 1

1 / 2 = 1 + remainder of 1

(2) Solution: 12510=11111012