1/6 | - 82% + A Converting Numbers to Decimal Equivalents A number in base b can be converted to its equivalent in base 10 by using place values. Place Value Formula b'b'b*b*b*bbbbbbbb Given 1394210, what do the individual digits represent? 13942 10 - 1(10)* + 3(10)' + 9(10)2 + 4(10)' + 2(10) = 10,000+ 3000 +900 +40 +2 Likewise, the digits in the base 2 number 110101 represent powers of the base 2. 110101 2-1(2) + (2)* +0(2) + 1(2) +0(2)+1(2) = 1(32)+1(16) +0(8) + (4) +0(2) +1(1) = 32 + 16 +0 +4 +0 + 1 = 5310 The same can be done for any other base such as converting 13F16 to base ten 13F16-1(16)* + 3(16) + F(16) 1(256) + 3(16) +15(1) = 256 +48 + 15 = 319.10 Or to converting 375x to base ten. 375, = 3(8)2 + 7(8) + 5(8) =3(64)+7(8) +5(1) = 192 +56 +5 -253 10 2 / 6 82% + L Converting Numbers to Decimal Equivalents Practice 1012 = 10102= 1011012 = 110101012 = 2716 13AD16 34178 = 11012 Converting from Binary to Hexadecimal Converting back and forth from binary to hexadecimal is straight forward. This is because 4 binary digits matches exactly with one hexadecimal digit. To covert from decimal to hexadecimal, just look up each hexadecimal digit and write out the equivalent set four binary digits. To go the other way, circle groups of four binary digits and write out the equivalent hexadecimal digit. This should be done from right to left and fill in any leading zero's 0000 Example 1: 8D316= 0010 D 3 1000 1101 0111 0001 8 0 1 2 3 4 $ 6 7 8 9 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 Example 2: 10001001100 ? 16 A B c D E F 0100 4 0101 5 1100 Converting from Binary to Hexadecimal Practice 1011011011101100010110112 1000111010111101011101100100101001012 A7F316 D239AE1 82% + Converting from Decimal to other Bases One way to do this is to repeatedly divide the decimal number by the base in which it is to be converted, until the quotient becomes zero. As the number is divided, the remainders - in reverse order - form the digits of the number in the other base. This is also referred to as the divide and conquer algorithm. Examples 173416 110110001102 173410 -6C616 173410 - 3306 O_R_ 0_R_6 O_R_3 21_R_1 16)6_R R_12 8)3_R_3 23_R_O 165108_R_6 8)27_R_0 2)6_R_1 1651734 8)216_R_6 2)13_R_ 8)1734 2)27_R_0 2)54_R_O 2)108_R_0 2)216_R_1 2)433_R_1 27867_R_0 2)1734 5 / 6 82% + Converting from Decimal to Base X Practice 4710 27410 = 771210 4542510 6 / 6 82% + 4710 = 8 27410 = 8 771210 = 4542510 16 16 771210 = 16 4542510 16 Bnaan