Write the numbers 8, 4, 2, and 1 in descending order. Binary numbers are formed by choosing numbers from this sequence and adding them together to form a number that is desired. The number 1 is used to choose numbers out of the ( 8, 4, 2, 1 ) sequence that are needed, and a zero replaces the numbers that are not needed. Each 1 or 0 used to form a binary number is referred to as a ” bit ” of information.
For example, using the ( 8, 4, 2, 1 ) template, the number 1 is formed by choosing 1 from the sequence and placing a zero in place of the other numbers. Number 1 in binary = ( 0001 ). The number 2 in binary = ( 0010 ), because the number 2 ( out of the 8, 4, 2, 1 sequence ) is the only number needed to form the number 2.
Trick question: How must binary 3 be obtained from the ( 8, 4, 2, 1 ) sequence? Since 2 + 1 = 3, we need the 2 and the 1 to be selected from the list. Binary 3 = ( 0011 ).
Q: How is the number ( 1111 ) expressed in the base-10 counting system?
A: 8 + 4 + 2 + 1 = 15.
Listed below are the numbers ( 0 to 15 ) expressed in binary:
0000 ( zero ); 0001 ( one ); 0010 ( two ); 0011 ( three ); 0100 ( four ); 0101 ( five ); 0110 ( six ); 0111 ( seven ); 1000 ( eight ); 1001 ( nine ); 1010 ( ten ); 1011 ( eleven ); 1100 ( twelve ); 1101 ( thirteen ); 1110 ( fourteen ); 1111 ( fifteen ).
NOTE: The counting system most familiar is the base-10 system. More than likely, the base-10 system is dominant due to human beings having 10 fingers. Actually, the base-10 system consists of the numbers 0 to 9. After the number 9 is passed, a 1 and 0 ( the number 10 ) are used to show that one complete counting cycle has transpired. After the number 10, another round of counting ensues until the number 19 and followed by another reset at number 20.
In the hexadecimal counting system ( HEX ), there are 16 digits; therefore, this system can be used to express the numbers 0 to 15 with more convenience; however, the first 16 digits of the hexadecimal system are expressed in the following manner:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F, with the number F = 15.
In the base-10 system, a counting reset occurs when the number 9 is passed. The F in the sequence above is the last digit in the hexadecimal counting system; thus, the number 16 in HEX is 10. Counting from 16 to 32 in HEX, we have the following:
10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1A, 1B, 1C, 1D, 1E, 1F, and 20.
Loosely speaking, a computer program can be regarded as binary number sequences stored in ROM, loaded to RAM, and read one by one according to how a programmer placed them into order. English letters are composed of different sequences of binary numbers, with eight-bit groups being referred to as a ” byte “. Bytes of information are stored in semiconductor circuits called ” registers “.
For further study, please reference the ” fetch, decode, execute cycle “.
RENAISSANCE PHYSICS 