Page 67 - Programmable Logic Controllers, Fifth Edition - Mobile version

Binary Bits
number 15 14 13 12 11 10 98 76 54 32 10
7 6 5 4 3 2 1 0 0000
0001
1 0 1 0 1 1 0 1
2 0002
0
1 × 2 = 1 × 1 = 1
1
0 × 2 = 0 × 2 = 0 0003
2
1 × 2 = 1 × 4 = 4 0004 01 10 01 10 00 111 01 1
3
1 × 2 = 1 × 8 = 8 0005
4
0 × 2 = 0 × 16 = 0
5
1 × 2 = 1 × 32 = 32 1018
6
0 × 2 = 0 × 64 = 0 1019
7
1 × 2 = 1 × 128 = 128 1020
Decimal number 173 10 1021
(Sum of products) 1022
Figure 3-3 Converting a binary number to a decimal number. 1023
Word
Addresses
are referred to as words. Each word is capable of storing Figure 3-5 1-K word memory.
data in the form of binary digits, or bits. The number of
bits that a word can store depends on the type of PLC sys-
tem used. Sixteen-bit and 32-bit words are the most com- there is a remainder, it is placed in the LSB of the binary
mon. Bits can also be grouped within a word into bytes. number. If there is no remainder, a 0 is placed in the LSB.
A group of 8 bits is a byte, and a group of 2 or more bytes The result of the division is brought down and the pro-
is a word. Figure 3-4 illustrates a 16-bit word made up cess is repeated until the result of successive divisions has
of 2 bytes. The least significant bit (LSB) is the digit that been reduced to 0.
represents the smallest value, and the most significant bit Even though the binary system has only two digits, it
(MSB) is the digit that represents the largest value. A bit can be used to represent any quantity that can be repre-
within the word can exist only in two states: a logical 1 (or sented in the decimal system. All PLCs work internally in
ON) condition, or a logical 0 (or OFF) condition. the binary system. The processor, being a digital device,
PLC memory is organized using bytes, single words, understands only 0s and 1s, or binary.
or double words. Older PLCs use 8-bit or 16-bit memory Computer memory is, then, a series of binary 1s and 0s.
words while newer systems, such as the ControlLogix plat- Figure 3-7 shows the output status file for an Allen-Bradley
form from Allen-Bradley, use 32-bit double words. The SLC 500 modular chassis, which is made up of single
size of the programmable controller memory relates to the bits grouped into 16-bit words. One or more 16-bit out-
amount of user program that can be stored. If the mem- put file word is reserved for each slot in the chassis. Each
ory size is 1 K word (Figure 3-5), it can store 1024 words bit represents the ON or OFF state of one output point.
or 16,384 (1024 × 16) bits of information using 16-bit
words, or 32,768 (1024 × 32) bits using 32-bit words. Decimal number
To convert a decimal number to its binary equivalent,
we must perform a series of divisions by 2. Figure 3-6 47 ÷ 2 = 23 with a remainder of 1 LSB
illustrates the conversion of the decimal number 47 to 23 ÷ 2 = 11 with a remainder of 1
binary. We start by dividing the decimal number by 2. If
11 ÷ 2 = 5 with a remainder of 1
5 ÷ 2 = 2 with a remainder of 1
MSB Bit LSB 2 ÷ 2 = 1 with a remainder of 0

0 1 1 0 0 1 1 0 0 0 1 1 1 0 1 1 1 ÷ 2 = with a remainder of 1 MSB
Upper byte Lower byte
Binary number 101111
16-bit word
Figure 3-6 Converting a decimal number to a binary
Figure 3-4 A 16-bit word. number.

48 Chapter 3 Number Systems and Codes

pet73842_ch03_046-060.indd 48 03/11/15 3:50 PM