1.8. Read and translate the text. Digital Computer Principles Binary Numbers

All digital computers work on the binary principle, that is, numbers or instructions are combinations of a basic bin­ary digit (a BIT) which can have only one or two possible states, e.g., 0 or 1; true or false; open or closed, etc. In order to represent larger numbers or more complex instructions, bits are organized inside the computer into fixed length groups. A fixed number of bits inside the machine is called a word. The more bits to a word, the greater the range of number that can be handled, eventually resulting in greater numerical accuracy.¹ In fact the choice of the number of bits to a word is a trade-off² between cost on one hand and accuracy and versatility on the other.

However, in communicating with the outside world, other than binary characters must be handled, i.e. the num­ber 724 would be typed (displayed) as 3 separate decimal digits, a seven, a two and a four. Add to the range of the decimal numbers the alphabet and any special characters such as plus, multiply etc. signs and a set of say 50 unique characters exists. Each of these characters could be uniquely represented by combinations of 6 bits (this gives 2⁶=64 possible characters). Thus a block of 6 bits is often used and called a character. More commonly, bits are grouped in 8's and called a byte. 8 bits allow not only for more than' 64 characters, but also for special coding to act in self checking of transmitted numbers. A commonly used 8 bit code is the ASCII code,³ although others exist.

Binary code decimal (B.C.D.) is another example of a number code. Each digit of the decimal number is coded as a four bit binary number. This is a wasteful code since 16 combinations can be made from 4 bits while only 10 are used.

Coded numbers are only necessary to ease the human understanding of the input/output of the computer. Thus the B.C.D. number transmitted to the computer must be decoded into a straight binary number (a computer word made up from a group of characters or bytes) before being processed in the computer.

Octal numbers, e.g. radix 8, rather than 2 (binary) or 10 (decimal) are often encountered, effectively as a shorthand method⁴ of writing binary numbers, since starting from the least significant, i.e. the right hand, each group of 3 bits represents one octal number in the range 0 — 7, thus 01110101100011₍2)= 16543₍₈₎

The conversion to decimal (7523) is more awkward! Serial and Parallel Numbers

In a machine with an n-bit word, the word can be stored and transmitted around the machine in one of two modes:

1. Serial, in which n bits are transmitted in sequence along a line and

2. Parallel, in which n lines, each carrying one bit, are used.

Serial operation requires n time "slots" and is thus slow. Parallel operation requires n lines and is therefore more expensive.

With high hardware costs, many earlier computers were serial machines, but the fall in hardware costs resulting from production of integrated circuits, means that all current machines should work in a parallel mode.