PLC - Chapter 3: Number Systems and Codes

The decimal system has a base of __.

The decimal number 7 would be written in binary as 1011.

To express a number in decimal requires fewer digits than in the binary system.

For a base 2 number system, the weight value associated with the 3rd digit would be 4.

Label the "Sign Bit" and the "Magnitude Bits"

What is the decimal value of binary 110010?

The decimal number 15 would be written in binary as

Data can be stored in one 16-bit word as two separate groups of 8-bit data.

To represent a negative number in 1's complement, you simply take the number's magnitude and flip all the bits (i.e. 1 becomes 0, and 0 becomes 1).

+3 binary representation: 0011 -3 binary representation: [blank_start]1100[blank_end] (1's complement)

The octal numbering system has a base of 9.

The weights for the octal numbering system are: 1, [blank_start]8[blank_end], [blank_start]64[blank_end], 512, ...

Numbers 8 and 9 are not allowed in the octal numbering system.

Fill in the missing number.

Convert this octal number to binary.

The hexadecimal numbering system can be summarized as follows: Sixteen digits: 0, 1, 2, 3, 4, 5, [blank_start]6[blank_end], [blank_start]7[blank_end], [blank_start]8[blank_end], [blank_start]9[blank_end], [blank_start]A[blank_end], [blank_start]B[blank_end], [blank_start]C[blank_end], [blank_start]D[blank_end], [blank_start]E[blank_end], [blank_start]F[blank_end]

The weights of the hexadecimal system are powers of base 16 (i.e. 1, 16, 256, etc.).

To convert a hexadecimal number to its decimal equivalent, the hexadecimal digits in the columns are divided by the base 16 weight.

Convert this hex number into binary.

The BCD (Binary-Coded Decimal) numbering system provides a convenient way of handling [blank_start]large[blank_end] numbers that need to be inputted to or outputted from a PLC.

Convert this decimal number into a BCD number.

This instruction will convert the binary bit pattern at the source address [blank_start]N7:23[blank_end], into a [blank_start]BCD[blank_end] bit pattern of the same decimal value as the destination address, [blank_start]O:20[blank_end]. The instruction executes every time it is scanned and the instruction is true.

The Gray code is a special type of binary code that uses position weighting.

ASCII stands for [blank_start]American[blank_end] [blank_start]Standard[blank_end] [blank_start]Code[blank_end] for [blank_start]Information[blank_end] [blank_start]Interchange[blank_end]. It is an alphanumeric code because it indicates letters as well as numbers.

Gray codes are used with [blank_start]position encoders[blank_end] for accurate control of the motion of robots, machine tools, and servomechanisms.

Some PLC communications systems use a [blank_start]parity[blank_end] bit to check the accuracy of data transmission. For example, when data are transferred between PLCs, one of the binary bits may accidentally change states.

The two systems of parity normally used are odd and even.

Odd parity means that the total number of binary 1 bits in the character, including the parity bit, is [blank_start]odd[blank_end]. Even parity means that the total number of binary 1 bits in the character, including the parity bit, is [blank_start]even[blank_end].

In the binary system + and – symbols are used to indicate whether a number is positive or negative.

The octal number 153 would be written in binary as:

What is the decimal equivalent for the BCD number 1000 0100 0010 0001?

The Gray code is set up so that as we progress from one number to the next, only one bit changes.

Which code is used to convert the keystrokes on the keyboard of a computer for the processor?

A parity bit is used to check the _______ of data transmission.

What is the sum of binary numbers 1100 and 1011?

Which instruction is used to compare the relative magnitude of two quantities?

The process for dividing one binary number by another is the same for both binary and decimal numbers.

Solve this.

Solve this.

Good luck, babe