# Relationship between binary hexadecimal and ascii values

### BBC Bitesize - GCSE Computer Science - Hexadecimal and character sets - Revision 3

A binary number consists of BInary digiTs (or “BITs”), each of which may be To form a hexadecimal number (with the same value), just group the bits four at a Unfortunately, when the ASCII standard (X–) was promulgated, the six. Decimal. Binary. Hex. Null. NUL. Ctrl @. 0. Start of Heading. SOH. Ctrl A. 1. Start of Text. STX. Ctrl B. 2. End of Text. Or easily identify byte values without having to look at binary's hypnotic string of you when you're learning about hexadecimal and its relationship to decimal.

The third position is the base squared, orand so on. Because the largest of the decimal system's 10 digits is 9, the greatest number that can be represented in the rightmost position is 9 9 X 1. The greatest number that can be represented in the second position, then, is 90 9 X In the third position, the greatest number isand so on.

Having placed the marbles in stacks of 10, Ralph knows immediately that there will be no need for a fourth-position digit the thousands position. It is apparent, however, that a digit must be placed in the third position.

Ralph must continue to the second position to represent the remaining 24 marbles. In each successive position, Ralph wants to represent as many marbles as possible.

There are still four marbles left to be represented. This can be done by inserting a 4 in the rightmost, or "ones," position. The combination of the three numbers in their relative positions represents decimal.

HEX, OCT, BCD, Grays, and ASCII

Ralph would go through the same thought process if asked to represent the decimal marbles using the binary numbering system see Figure 3.

To make the binary conversion process easier to follow, the computations in Figure 3 are done in the more familiar decimal numbering system. See if you can trace Ralph's steps as you work through Figure 3.

FIGURE 3 Representing a Binary Number To represent marbles in binary, we would follow the same thought process as we would in decimal see Figure 2but this time we have only two digits 0 and 1. For ease of understanding, the arithmetic is done in decimal. Hexadecimal Perhaps the biggest drawback to using the binary numbering system for computer operations is that programmers may have to deal with long and confusing strings of 1s and 0s.

To reduce the confusion, the hexadecimal, or base, numbering system is used as shorthand to display the binary contents of primary and secondary storage.

Notice that the bases of the binary and hexadecimal numbering systems are multiples of 2: Because of this, there is a convenient relationship between these numbering systems. Notice that in hexadecimal, or "hex," letters are used to represent the six higher order digits.

We will now examine how to convert one number in a numbering system to an equivalent number in another numbering system. For example, there are occasions when we might wish to convert a hexadecimal number into its binary equivalent.

We shall also learn the fundamentals of numbering-system arithmetic. This two-step technique is illustrated in Figure 5. Follow these steps to convert decimal to binary. Divide the number 19, in this example repeatedly by 2, and record the remainder of each division. In the first division, 2 goes into 19 nine times with a remainder of 1.

The remainder is always one of the binary digits or 1. In the last division you divide 1 by the base 2 and the remainder is 1. Rotate the remainders as shown in Figure 5; the result is the binary equivalent of a decimal In a decimal-to-hex conversion, the remainder is always one of the 16 hex digits. Binary to Decimal and Hexadecimal To convert from binary to decimal, multiply the 1s in a binary number by their position values, then sum the products see Figure 7.

In Figure 7, for example, binary is converted into its decimal equivalent The easiest conversion is binary to hex. To convert binary to hex, simply begin with the 1s position on the right and segment the binary number into groups of four digits each see Figure 8.

Refer to the equivalence table in Figure 2, and assign each group of four binary digits a hex equivalent. Combine your result, and the conversion is complete.

Hexadecimal to Binary To convert hex numbers into binary, perform the grouping procedure for converting binary to hex in reverse see Figure 8. Hexadecimal to Decimal Use the same procedure as that used for binary-to-decimal conversions see Figure 7 to convert hex to decimal.

An error will occur when data is stored in Big Endian by one computer and read in Little Endian format on another. Boolean information A boolean number is has two states. The two values could represent the logical true or false. The positive logic representation defines true as a 1 or high, and false as a 0 or low. If you were controlling a motor, light, heater or air conditioner the boolean could mean on or off.

### ASCII Character Chart with Decimal, Binary and Hexadecimal Conversions

In communication systems, we represent the information as a sequence of booleans: For black or white graphic displays we use booleans to specify the state of each pixel. The most efficient storage of booleans on a computer is to map each boolean into one memory bit.

In this way, we could pack 8 booleans into each byte. If we have just one boolean to store in memory, out of convenience we allocate an entire byte or word for it.

Most C compilers including Keil uVision define: False be all zeros, and True be any nonzero value. Many programmers add the following macros define TRUE 1 Decimal Numbers Decimal numbers are written as a sequence of decimal digits 0 through 9. The number may be preceded by a plus or minus sign or followed by a Lor U.

Lower case l or u could also be used. The minus sign gives the number a negative value, otherwise it is positive. The plus sign is optional for positive values.