Binary, HEX & ASCII Study Guide

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To represent the value requires eight binary digits. The decimal version requires only three decimal digits and, thus, represents numbers much more compactly than does the binary numbering system. This fact was not lost on the engineers who designed binary computer systems. Binary to hex table dealing with large values, binary numbers quickly become too unwieldy. The hexadecimal base 16 numbering system solves these problems. Hexadecimal numbers offer the two features:.

Since we'll often need to enter hexadecimal numbers into the computer system, we'll need a different mechanism for representing hexadecimal numbers since you cannot enter a subscript to denote the radix of the associated value.

The Hexadecimal system is based on the binary system using a Nibble binary to hex table 4-bit binary to hex table. In Assembly Language programming, most assemblers require the first digit of a hexadecimal number to be 0, and we place an H at the end of the number to denote the number base. In the Hexadecimal number system, the hex values greater than 9 carry the following decimal value:. To convert a hexadecimal number into a binary number, simply brake the binary number into 4-bit groups beginning with the LSB and substitute the corresponding four bits in binary binary to hex table each hexadecimal digit in the number.

For example, to convert 0ABCDh into a binary value, simply convert each hexadecimal digit according to the table above. The binary equivalent is:. To convert a binary number into hexadecimal format is almost as easy. The first step is to pad the binary number with leading zeros to make sure that the the binary number contains multiples of four bits.

For example, given the binary number 10the first step would be to add two bits in the MSB position so that it contains 12 bits. The revised binary value is The next step is to separate the binary value into groups of four bits, e.

Finally, look up these binary values in the table above and substitute the appropriate hexadecimal digits, e. A F B binary to hex table This yields the binary number or in our more readable format. To convert from Hex to Decimal, multiply the value in each position by its hex weight and add each value.

Using the value from the previous example, 0AFB2H, we would expect to obtain the decimal value To convert decimal to hex is slightly more difficult. The typical method to convert from decimal to hex is repeated division by While we may also use repeated subtraction by the weighted position value, it is more difficult for large decimal numbers.

For this method, divide the decimal number binary to hex table 16, and write the remainder on the side as the least significant digit. This process is continued by dividing the quotient by 16 and writing the remainder until the quotient is 0.

When performing the division, the remainders which will represent the hex equivalent of the decimal number are written beginning binary to hex table the binary to hex table significant digit right and each new digit is written to the next more significant digit the left of the previous digit. Consider the number That is what we should expect. When you use hex numbers in an program, the Assembler usually requires the most significant hex digit to be 0 even if this number of digits binary to hex table the size of the register.

This is an Assembler requirement and your value will be assembled correctly.

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Binary to Hex Conversion This conversion can be done by grouping of binary bits method. The below steps may useful to know how to perform binary to hex conversion. Separate the digits into groups from right to left side.

Each group should contain 4 bits of binary number. Add 0's to the left, if the last group doesn't contain 4 digits. Find the equivalent hexadecimal number for each group. Write the all groups hexadecimal numbers together, maintaining the group order provides the equivalent hex number for the given binary. Solved Example Problem The below solved example problem may useful to understand how to perform binary to hex number conversion.

Problem Convert the binary number 2 to its hexadecimal equivalent. This conversion can be done by finding the binary equivalent for an each digit of the hex number, combining them together in the same order. The below steps may useful to know how to perform hex to binary number conversion.

Separate the digits of the given hexadecimal, if more than 1 digit. Find the equivalent binary number for each digit of hex number, add 0's to the left if any of the binary equivalent is shorter than 4 bits. Write the all groups binary numbers together, maintaining the same group order provides the equivalent binary for the given hexadecimal.

Solved Example Problem The below solved example problem may useful to understand how to perform hex to binary number conversion. Problem Convert the hexadecimal 9DB. A5 16 to its binary equivalent. Numbers Conversion Table Decimal Binary Octal Hex 0 0 0 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 10 8 9 11 9 10 12 A 11 13 B 12 14 C 13 15 D 14 16 E 15 17 F. Binary - Hex Converter. Binary - Hex Conversion. Binary to Hex Hex to Binary. BCD to Decimal Converter. Binary - Decimal Converter. Binary - Gray Code Converter.

Binary - Octal Converter. Decimal - Octal Converter.