Draw the input-output voltage transfer characteristic of a digital logic gate

What benefit does the voltage transfer characteristic of a digital logic gate have?

It makes small inputs become very small outputs, large inputs become very large outputs and medium stay the same. This has the effect of pushing signals towards either high or low, thus creating a more discrete signal and reducing overall **noise **and also outwith the non-logic region.

Show on a graph what the rising and falling transition times for a CMOS device

What is in between the logic high and logic low regions?

The logic invalid region. The system is designed to not use the output during this time.

Show on a graph what the input to output propagation delay for a series of gates is.

Where is it measured from?

When the imput crosses 50% to the output crosses 50%.

What is the third logic value and what does it mean?

*

Represents "don't care"

How many of codewords are possible in an N bit binary code?

What do you call a code that uses less than half of these possible codewords and what could you do about it?

There are 2^{N} possible codewords.

A code which uses less than half of the codewords is **sparse**, otherwise it is **dense**. This means it could be encoded to use fewer bits if desired.

Describe the Thermometer code.

Sparse or Dense?

Hamming Distance?

Sparse code.

Unit distance.

Describe the Gray Code.

Sparse or dense?

Hamming distance?

Dense code

Unit-distance circular code

How many bits in each ASCII codeword?

Dense/sparse?

What do the 32 codewords starting 00***** represent?

Is the alphabet in natural order?

What about numbers?

A 7-bit code for communicating graphical symbols

Dense code

Non-graphic symbols such as return

Yes. 1000001 (A), 1000010 (B), etc

Yes. 0110000 (0), 0110001 (1), etc

Describe the BNN (Binary Natural Number) code

Range?

Resolution?

Similar to base-2 notation but 1 is true instead of one and 0 is false not zero.

Range: 0 to (2^{N} - 1)

Resolution: uniform, unity

Describe the SM (Sign Magnitude) number code.

Range?

Resolution?

Essentially BNN but an extra bit to *multiply* result by -1

Range: -(2^{(N-1)} - 1) to +(2^{(N-1)} - 1)

Resolution: uniform, unity

Describe the 1'sC (One's complement) number code.

Range?

Resolution?

For positive values (first bit is 0) is just BNN

For negative values (first bit is 1) then invert remaining bits and take BNN.

Range: -(2^{(N-1)} - 1) to +(2^{(N-1)} - 1)

Resolution: uniform, unity

Describe the offset BNN code

Range?

Resolution?

Add a positive **bias** constant to the valu eto be encoded then encode with BNN. To get the value from the codeword subtract the **bias** from the BNN value of the codeword.

Range: Total is 2^{N}, limits set by **bias**

Resolution: uniform, unity

Describe the 2'sC (Two's Complement) number code.

Resolution?

Range?

Like BNN but most significant bit has negative value

Range: -2^{(N-1)} to 2^{(N-1)} - 1

Resolution: uniform, unity

Describe the fixed point number code, including what F fractional bits means.

Range?

Resolution?

There is a "fraction point" which splits the bits into F fractional bits and N-F other bits. Is usually used with the other codes such as BNN, 2'sC, etc.

Range: 0 to approx 2^{N-F} + 1

Resolution: uniform, 2^{-F}

Describe the Binary Coded Decimal (BCD) number code.

When would you use it over the more conventional codes?

A code within a code.

Split the code into 4-bit fields each of which is used to represnt a single decimal digit 0-9. Thus there are 6 unused codewords (10-15).

Useful for legally exact financial calculations, where very little arithmetic processing is needed.

Describe the IEEE 754-1985 floating-point number code, mentioning the three fields, the number of bits in them and how the value is calculated.

- The sign
**1 bit** - The exponent
**8 bits** - The mantissa
**23 bits**

*value *= ( -1 )^{sign} x 2^{exponent - 127 }x 1.*significand *

An exponent of -127 or 128 are reserved for special codewords such as NaN, infinity, zero