Introduction to Number Representation

Binary Coded Decimal (BCD)

• BCD represents denary integers using blocks of four binary digits.
• Each block of four is converted and the denary values are then read off:
• Therefore 1001 0011 1000 in BCD = 938 in denary.

8	4	2	1
1	0	0	1
8 + 0 + 0 + 1
9

8	4	2	1
0	0	1	1
0 + 0 + 2 + 1
3

8	4	2	1
1	0	0	0
8 + 0 + 0 + 0
8

Uses of BCD

• BCD enables fast conversions from denary to binary for applications such as pocket calculators.
• Each digit on a calculator corresponds directly to a four-bit block in BCD.

Storing Negative Integers

• 1 method is Sign/Magnitude

	64	32	16	8	4	2	1

• 128

• +/-

• MSB

• 0

• 1

• 0

• 0

• 1

• 0

• 1

• 1

• 75
• -75

• 1

• 1 is a Negative, 0 is a Positive

Sign/Magnitude

• This method has some limitations
• Makes calculations difficult by losing 1 bit

	64	32	16	8	4	2	1

• +/-

• 0

• 1

• 0

• 0

• 1

• 0

• 1

• 1

• 127 maximum number

• Sign

• Value or Magnitude

Storing Negative Integers

• Another method is 2s Complement

	64	32	16	8	4	2	1

• 128

• -128

• 1

• 0

• 1

• 1

• 0

• 1

• 0

• 1

• -75

• -128+32+16+4+1=-75

2s Complement Conversion

• -117
• Stage 1 : work out 117 in binary

-128	64	32	16	8	4	2	1
1	0	0	0	1	0	1

• Stage 2 : Reverse the 0’s and 1’s

128	64	32	16	8	4	2	1
0	1	1	1	0	1	0	1

• Stage 3 : Plus 1

• 1

• 0

Representing characters

• There are three main coding systems that provide conversions of keyboard characters into binary:
• EBCDIC
• ASCII
• UNICODE

EBCDIC

• EBCDIC stands for Extended Binary Coded Decimal Interchange Code.
• It is an extension of BCD which includes non-numeric characters, including all the keyboard characters and special characters.
• It is commonly used to encode data onto magnetic tape.

ASCII

• ASCII stands for the American Standard Code for Information Interchange.
• It has been adopted as the industry-standard way of representing keyboard characters as binary codes.
• Every keyboard character is given a corresponding binary code.
• ASCII uses an 8-bit code to provide 256 characters.

UNICODE

• UNICODE is the new standard to emerge that is replacing ASCII.
• It has been adopted by many of the big businesses in the computing industry.
• It is designed to cover more of the characters that are found in languages across the world.
• It has become important due to the increased use of the Internet, as more data is being passed around globally.