2.3: Information Representation

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All information, including numbers, characters, and instructions are represented in the computer in binary (1's and 0's). The information, numbers in this example, is converted into binary representation (1's and 0's) for storage in the computer. Fortunately, this is generally done transparently.

Decimal Numbers

Before discussing binary numbers, a brief review of the decimal system is presented. The number "1234" as,

Thousands	Hundreds	Tens	Ones
\(10^3\)	\(10^2\)	\(10^1\)	\(10^0\)
1000	100	10	1
1	2	3	4

Which means,

\(1234 = 1 \times 1000 + 2 \times 100 + 3 \times 10 + 4 \times 1\)

\(1234 = 1 \times 10^3 + 2 \times 10^2 + 3 \times 10^1 + 4 \times 10^0\)

The decimal system is base 10 using the digits 0 through 9.

Binary Numbers

A bit is the basic unit of information in computing and digital communications. A bit can have only one of two values, 0 or 1. The term bit is a contraction of binary digit.

The binary system, as well as its math, operates in base 2, using two symbols, 0 and 1

\(2^7\)	\(2^6\)	\(2^5\)	\(2^4\)	\(2^3\)	\(2^2\)	\(2^1\)	\(2^0\)
128	64	32	16	8	4	2	1
0	0	0	0	1	1	0	1

In base 2, we put the digits 0 or 1 in columns \(2^0\), \(2^1\), \(2^3\), and so on. For example,

\(1101_2 = 1 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 8 + 4 + 1\)

Which in decimal is \(13_{10}\).

A set of 8 bits is a referred to as a byte. Computer data is typically allocated in bytes or sets of bytes

Character Representation

Characters are represented using the American Standard Code for Information Interchange (ASCII). Refer to Appendix A.