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For example, the binary number 100101 is converted to decimal form as follows: 100101 2 = [ ( 1 ) × 2 5 ] + [ ( 0 ) × 2 4 ] + [ ( 0 ) × 2 3 ] + [ ( 1 ) × 2 2 ] + [ ( 0 ) × 2 1 ] + [ ( 1 ) × 2 0 ]
In computer science, the double dabble algorithm is used to convert binary numbers into binary-coded decimal (BCD) notation. It is also known as the shift-and-add-3 algorithm, and can be implemented using a small number of gates in computer hardware, but at the expense of high latency.
In computing and electronic systems, binary-coded decimal (BCD) is a class of binary encodings of decimal numbers where each digit is represented by a fixed number of bits, usually four or eight. Sometimes, special bit patterns are used for a sign or other indications (e.g. error or overflow).
In the decimal encoding, it is encoded as a series of p decimal digits (using the densely packed decimal (DPD) encoding). This makes conversion to decimal form efficient, but requires a specialized decimal ALU to process. In the binary integer decimal ( BID) encoding, it is encoded as a binary number.
For example, to calculate the decimal number −6 in binary from the number 6: Step 1: +6 in decimal is 0110 in binary; the leftmost significant bit (the first 0) is the sign (just 110 in binary would be -2 in decimal). Step 2: flip all bits in 0110, giving 1001. Step 3: add the place value 1 to the flipped number 1001, giving 1010.
Computer engineers often need to write out binary quantities, but in practice writing out a binary number such as 1001001101010001 is tedious and prone to errors. Therefore, binary quantities are written in a base-8, or "octal", or, much more commonly, a base-16, "hexadecimal" (hex), number format. In the decimal system, there are 10 digits, 0 ...
Binary-coded decimal. Binary-coded decimal (BCD) is a binary encoded representation of integer values that uses a 4-bit nibble to encode decimal digits. Four binary bits can encode up to 16 distinct values; but, in BCD-encoded numbers, only ten values in each nibble are legal, and encode the decimal digits zero, through nine.
Decimal Binary Gray 0: 0000: 0000: 1: 0001: 0001: 2: 0010: 0011: 3: 0011: 0010: 4: 0100: 0110: 5: 0101: 0111: 6: 0110: 0101: 7: 0111: 0100: 8: 1000: 1100: 9: 1001: 1101: 10: 1010: 1111: 11: 1011: 1110: 12: 1100: 1010: 13: 1101: 1011: 14: 1110: 1001: 15: 1111: 1000
This example shows the conversion of a binary number to decimal, mapping each digit to the decimal value, and adding the results. (01011110101101010010) 2 = 262144 10 + 65536 10 + 32768 10 + 16384 10 + 8192 10 + 2048 10 + 512 10 + 256 10 + 64 10 + 16 10 + 2 10
For writing numbers, the decimal system uses ten decimal digits, a decimal mark, and, for negative numbers, a minus sign "−". The decimal digits are 0 , 1 , 2, 3, 4, 5, 6, 7, 8, 9; [5] the decimal separator is the dot " . " in many countries (mostly English-speaking), [6] and a comma " , " in other countries.