The Bit Budget Begriff

– All computer storage is finite. —*

1. FIXED BIT BUDGETS:

Understanding the bit allocation in software or hardware as a bit budget: with a bit budget of n bits, any one of 2ⁿ different values can be stored (range from 0 through 2ⁿ-1). In other words, n bits makes 2ⁿ unique different addresses possible.

• For example, with a bit budget of 12, 4096 different unique numbers or addresses (bit combinations, from zero through 4095) can be stored (in registers or protocol fields).
• For example, with a bit budget of 4, I can support enough unique addresses for 14 subnets (CIDR addressing, 2ⁿ-2 subnets (for subnets, always subtract the 2 addresses consisting of all 1s (broadcast) and all 0s (current environment); 2⁴ = 16; 16–2 = 14).
• If I need to store 4096 different numbers or store any number or address greater/higher than 4095, my budget is not adequate and I need a larger budget.
• A bit budget can be established for a register, an address, a bus, or a protocol field. Fixed bit budgets are established for particular technologies (address fields in data communications and networking protocols, registers in processors). Bit budgets have to be calculated in applications such as DVDs, where the bit requirement of a particular DVD is determined for that DVD.
• Bit budgets are associated with different ($, £, ¥, €) costs for different size registers, address operands for commands, message header address components, or buses.
• A register that can hold 32 bits has a bit budget of 32; a network protocol address field that can hold 3 bits has a bit budget of 3.
• Underlying bit budgets determine the maximum size of identifiers and values in standard programming and database languages.

Note that all computer storage is finite!*

There will be a maximum size (extent) for any storage requested. All bit values are shown – Here is a storage space (or data communications protocol field) with a bit budget of 8:

overflow	0	0	1	0	1	1	0	1	truncation
	high-order bit, most significant bit							low-order bit, least significant bit

2. BIT BUDGETS AND LARGEST NUMBERS/HIGHEST ADDRESSES:

· How many different numbers (addresses, bit patterns, or bit combinations) can be stored with a bit budget of… ?
2, 3, 4, 5, 6, 7, 8, 16, 32, 64, or 128 bits

· What is the largest number or highest address (hint: 1 less than number of different bit combinations based on bit budget allocation) that can be stored with this bit budget?
2, 3, 4, 5, 6, 7, 8, 16, 32, 64, or 128 bits:

3. ESTABLISHED BIT BUDGETS for PARTICULAR (standardized or proprietary) TECHNOLOGIES:

What are the bit budgets for… ?

o an ASCII byte

o an EBCDIC byte

o a UCS/Unicode character

o an octet

o Bluetooth “active slave” address (INFS3230, INFS6230)

o MAC address OUI octets (Organization Unique Identifier)

o Ethernet address

o Port Number (UDP or TCP, Internet)

o an IPv4 address

o an IPv6 address

o registers in Burd Ch. 4 (INFS2210, INFS6210)

o IEEE 802.1Q VLAN identification tag for frame (INFS4410, INFS6230)

o IEEE 802.1p bits in IEEE 801.1Q header to assign Class of Service (CoS) (INFS4410, INFS6230)

o Differential Services Code Point (DSCP) prioritization using bits from IP header Type of Service (ToS) octet (INFS4410, INFS6230)

o “Kind of Option” field in TCP header options (INFS6230) What is the maximum number of options supported?

o “Maximum Segment Size” length field in TCP header MSS option (INFS6230) What is the highest maximum segment size supported?

Example:

o CSMA/CD Extreme Networks – see Stephen Haddock at http://grouper.ieee.org/groups/802/3/z/public/presentations/sep1996/SHbitbud.txt

4. VARIABLE or CALCULATED BIT BUDGETS for PRACTICAL APPLICATIONS:

o DVDs – see Joe Clark on “Bit Budget Myths,” at http://www.joeclark.org/access/dvd/finer-points.html#bitbudgetmyths – examples of DVD bit budgets are provided, definition of bit budget for DVD applications is given

o See also a bit budget calculator for DVDs at http://www.customflix.com/Special/AuthoringNightmares/03/BitBudget.jsp (CustomFlix)

5. BIT BUDGETS and HEX REPRESENTATION:

Note that with a bit budget of 4 bits you can store 4-bit numbers in each hex digit location. You can then represent each number (4-bit address) with a single hex digit (ratio 4 bits to 1 hex digit or 4:1).

6
0	1	1	0

Example for 8 bits (2 hex digits) – 2D₁₆ = 00101101₂:

2				D
0	0	1	0	1	1	0	1

o How many hex digits does it take to represent a binary number stored according to a bit budget of… ?
4, 16, 32, 64, or 128 bits

* in today’s dominant computer technologies.

Contact: Valerie J. Harvey, RT(R), PhD, C&IS, RMU
As of: 2008-10-25
Copyright 1998-2005 by RMU