# Convert The Following To Their Required Bases

Convert the following base ten number to a number in the indicated base?

342

How do I convert the following base 5 number: 1432.14 to binary, decimal and 8421 BCD?

How do I convert the following base 5 number: 1432.14 to binary, decimal and 8421 BCD?Consider the decimal number 361.42. Decimal means that we are using base 10 numbers.[math]361.42 = 300 + 60 + 1 + 0.4 + 0.02[/math][math]= 3 \times 10^2 + 6 \times 10^1 + 1 \times 10^0 + 4 \times 10^{-1} + 2 \times 10^{-2}[/math]Now, let’s look at the base 5 number in your question and convert it into decimal format:[math]1432.14_5 = 1 \times 5^3 + 4 \times 5^2 + 3 \times 5^1 + 2 \times 5^0 + 1 \times 5^{-1} + 4 \times 5^{-2}[/math][math]= 125 + 4 \times 25 + 3 \times 5 + 2 + 0.2 + 4 \times 0.04[/math][math]= 125 + 100 + 15 + 2 + 0.2 + 0.16[/math][math]= 242.36_{10}[/math][math]\\[/math]Now for binary:[math]242.36_{10} = 128 + 64 + 32 + 16 + 2 + 0.25 + 0.0625 + 0.03125 + 0.015625 + 0.00048828125 +\ smaller terms[/math][math]= 2^7 + 2^6 + 2^5 + 2^4 + 2^1 + 2^{-2} + 2^{-4} + 2^{-5} + 2^{-6} + 2^{-11} +\ smaller\ terms[/math][math]= 11110010.01011100001 ...[/math][math]\approx 11110010.01011100_2[/math]There is no exact representation of 242.36 in binary - just like there is no exact representation of, say one twenty third in decimal.[math]\\[/math]Binary coded decimalEach digit of the decimal number is converted into a 4 byte decimal block, e.g. 9 is converted to 1001[math]\begin{bmatrix} Base 10 & BCD \\ 2 & 0010 \\ 4 & 0100 \\ 2 & 0010 \\ 3 & 0011 \\ 6 & 0110 \end{bmatrix}[/math]I’m assuming that BCD uses decimal points in the same manner as normal numbers.0010 0100 0010.0011 0110

How do I convert the following base 10 number, 42.25 to binary with fractional parts accurate to 4 BITS?

Answer: 101010.0100.See the procedure …Sanjay C.

Convert the following numbers to decimal?

In any base the position on the far right is the 1s position. Each position moving left is the previous position times the base. For example, in base 10 you have the 1s, 10s, 100s,1000s, etc. In base 2 you have 1s, 2s, 4s, 8s, 16s, etc. For bases above 10 the letters are used to represent the digits where A=10, B=11, etc.

In your example, 34 in base 8 is 3x8 + 4x1 = 28 decimal

AF in base 16 is 10x16+ 15x1 = 175 decimal

How to convert the following (unsigned) decimal numbers to the indicated bases?

Just repeatedly divide by the base with integer quotient and remainder, until you get a zero quotient. The remainders are the digits in the new base, in right to left order.

One way to do fractions, is to premultiply by a power of the base to get an integer first, and then perform the above method. The exponent in that power of the base is the number of fraction digits in the result.

This works for the first two problems. In the first, multiply by 8^1=8 to get

276, and convert by divison:

276/8 = 34 R 4

34/8 = 4 R 2

4/8 = 0 R 4

The digits are 424, with one fraction digit, giving 424.8 as base 8 fraction.

Do the same for problem 2.

In the third problem, there's no power of 2 that you can multiply by 0.6 = 3/5 to get an integer. The binary fraction will be infinitely repeating. The integer part is easily 32 + 16 + 4 + 2 + 1, or 11011 in binary. Convert 0.6 by repeatedly multiplying by 2, noting and then discarding the whole part. The discarded whole parts are the digits of the fraction in left to right order.

0.6*2 = 1.2

0.2* 2 = 0.4

0.4*2 = 0.8

0.8*2 = 1.6

0.6*2 = 1.2 .... and here you can see the 1001 pattern repeats

The final fraction is 110111.(1001) ... where the parenthesized fraction digits repeat forever (can't draw a bar above them.)

Another is to convert the integer part only, as above, and then convert the fraction by multiplication.

How do I convert 140336 base 8 to binary?

To answer this question I presume that you do not have much knowledge on Number Conversion. So I'll describe the answer from a novice point of view.This question can be answered by 2 methods.Method 1: First convert the number 140336 to it's decimal equivalent. The way to do that is you multiply each digit of the number starting from the ones position (in this case 6) with 8^n, where n>=0. So in this case we will have the decimal equivalent as=(6*8^0)+(3*8^1)+(3*8^2)+(0*8^3)+(4*8^4)+(1*8^5)=(6*1)+(3*8)+(3*64)+(0*512)+(4*4096)+(1*32768)=6+24+192+0+16384+32768=49374, which is the decimal equivalent of 140336.Now we can convert the decimal number 49374 to binary by using repeated division method. The way to do that is you divide the decimal number with 2(in this case 49374) and store the quotient and remainder. In the next step divide the previously stored quotient again with 2 and again store it's quotient and remainder. Continue this process till the quotient becomes 0. Hence the binary equivalent of 49374 can be calculated as49374= (2*24687) + 024687= (2*12343) + 112343= (2*6171) + 16171=(2*3085) + 13085= (2*1542) + 11542= (2*771) + 0771= (2*385) + 1385= (2*192) + 1192= (2*96) + 096= (2*48) + 048= (2*24) + 024= (2*12) + 012= (2*6) + 06= (2*3) + 03= (2*1) + 11= (2*0) + 1Notice that I have written the reminders a bit separately as because we need that for the final answer. Now after we have got all the remainders the next step is to write those sequence of remainders from the bottom to top. This will result in the required binary answer you want. As in this case we have the binary equivalent as 1100000011011110.Method 2: This is a short cut method and to use this method you need to know the binary equivalents of the numbers from 0 to 7. If you don't know I have mentioned it below as follows:0= 0001= 0012= 0103= 0114= 1005= 1016= 1107= 111Now to get the binary equivalent you just need to replace the digits of the octal number with it's corresponding binary equivalent. Hence the binary representation of the octal number 140336 will be 001 100 000 011 011 110. As you can see there are 2 zeros at the starting which you can obviously exclude. So the binary equivalent we got as 1100000011011110.

Converting expressions to indicated base?

2^x using base e.

I have no clue how to do this, I don't think I ever learned this in algebra but I am really good at math. Can someone explain how to do it? Thanks!

How do you convert from base 7 to base 5 without converting base 7 to base 10?

How do you convert from base [math]10[/math] to base [math]b[/math]?You have your (integer) decimal and divide the number through [math]b[/math]until you get [math]0[/math] and you take the reminders as the digits for base [math]b[/math], for example:[math]35[/math] in base [math]8[/math] can be calculated as:35 : 8 = 4 Reminder: 34 : 8 = 0 Reminder: 4Therefor [math]35=43_{8}[/math]This works for all bases, and if you can divide by [math]5[/math] in base [math]7[/math] with reminder, you can convert directly.But I would say it is easier to convert a base [math]7[/math] number to base [math]10[/math] first, your time saving by relearning division in base [math]7[/math] should be negligible.