Table I
MSD Addition Six Possible Bit-Pair Carries and Sums
| 1 |
| 0 | 1 | 0 | 0 |
|---|
| + | 1 |
| 0 |
| 1 |
|
|---|
| carry | 1 |
| 0 | 0 | 0 | or | 1 | 0 | or |
|
| sum | 0 | 0 | 0 | 0 | 1 |
|
| 1 |
Table II
First MSD Addition Conditional Symbolic Substitution Rule Truth Table for Rearranging Data: T+(W+), the Corresponding Transfer (Weight) Operator
Table III
Second MSD Addition Bit-wise Symbolic Substitution Rule Truth Table: A (C), the Sum (Complement of the Sum) Operator
Table IV
First MSD Subtraction Conditional Symbolic Substitution Rule Truth Table [Converting the Subtraction to Addition Operation and Rearranging the Addition Data: T−(W−), the Corresponding Transfer (Weight) Operator]
Table V
Reduced Logic Minterm Expressions for the Implementation of the MSD Addition and Subtraction Operations. The × Denotes a Do Not Care as Specified in Table VII. The Four Variable Minterm is Grouped as
| MSD logic | bit | reduced |
|---|
| product | term |
|---|
|
|---|
| T+ | 1 | 1X | 1X01 | 0X01 |
| 1X, | 0X01, | 1X01 |
|
|
X |
| 0
|
|
X, | 0
, |
|
| T− | 1 | 1X | 1X01 | 0X01 |
|
X, | 0
, |
|
|
|
X |
| 0
|
| 1X, | 0X01, | 1X01 |
| A | 1 | 1 | 0 |
| 0, | 1 |
|
|
| 0 |
| 0, |
|
| W+ | 1 | 1
1X | 0
0X |
0
|
| 0X,0
| 1X,1
| 0
,
|
|
|
1
X | 01 0X | 1X01 0X01 |
| 0X,01, |
X,
1 | 0X01,1X01 |
| W− | 1 | 1
1X | 0
0X |
0
|
| 0X,01 |
X,
1 | 0X01,1X01 |
|
| 01 0X |
1
X | 1X01 0X01 |
| 1X,1
| 0X,0
| 0
,
|
| C | 1 | 0 |
|
|
, | 0 |
|
| 0 | 1 |
| 1, | 0 |
Table VI
Comparison Among the One-, Two- and Three-Step N-bit CAM MSD Addition Schemes. In Terms of Processing Speed, the One-Step Method is the Fastest, While in Terms of the Product of the Speed and Total Number of References, the Two-Step Method is the Optimum.
| methods | No. of CAMs | No. of refs. for each CAM | total No. of refs. | normalized speed |
|---|
| 1-step | N + 1 | ⩽56 | 56N − 74 | T |
| 2-step | 3N − 1 | ⩽12 | 22N − 4 | 2T |
| 3-step | 5N − 3 | ⩽4 | 18N − 10 | 3T |
Table VII
Various MSD Do Not Care Types and Their Corresponding Spatial Encoding: m, n, and E Denote the Number of Nonzero, the Number of Do Not Care Bits, and the Single General Reference Bit Exposure, Respectively.
| dont care type | patterns to be recorded | Rt(w)-bit exposure |
|---|
| ○-phase | π-phase |
|---|
|
|---|
| X |
 |
| mE |
|
|
 |
| mE |
| X0 1 |
 |
| mE |
|
|
|
 | (m+n) E |
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