punctuation and typos

M17_spec.tex

@@ -1303,7 +1303,7 @@ Unlike Text and Extended Callsign Data, GNSS data is expected to be dynamic duri
 
 The GNSS data fits within one 14-byte META field, which equates to six audio frames, and takes 240ms to transmit. This is a simple format of the GNSS data which does not require too much work to convert into, and provides enough flexibility for most cases. This has been tested on-air and successfully gated to APRS-IS, showing a location very close to the position reported by the GPS receiver.
 
-The GNSS data includes eight numeric values using from $3$ bits to $24$ bits. The two largest $24$ bit values are signed, two's complement values while the other six are unsigned values. All numeric fields are in order from most significant to least significant bit. There is also one $4$ bit validity field that used to indicate which numeric fields are valid.
+The GNSS data includes eight numeric values using from $3$ bits to $24$ bits. The two largest $24$ bit values are signed, two's complement values. The other six are unsigned values. All numeric fields are in order from most significant to least significant bit. There is also one $4$ bit validity field that used to indicate which numeric fields are valid.
 
 GNSS Position Data uses the 112 bit (14 byte) META field as follows:
 
@@ -1365,7 +1365,7 @@ GNSS Position Data uses the 112 bit (14 byte) META field as follows:
 	\caption{GNSS Data encoding}
 \end{table}
 
-The first byte contains two $4$ bit numeric fields. The first is the \textbf{Data Source} where: $0$ is an M17 client, $1$ is OpenRTX and $15$ is "other" while values $2..14$ are reserved. The second $4$ bit field is \textbf{Station Type}, where $0$ is a fixed station, $1$ is a mobile station, $2$ is a handheld and $15$ is "other". Values $3..14$ are reserved. 
+The first byte contains two $4$ bit numeric fields. The first is the \textbf{Data Source} where: $0$ is an M17 client, $1$ is OpenRTX and $15$ is "other", while values $2..14$ are reserved. The second $4$ bit field is \textbf{Station Type}, where $0$ is a fixed station, $1$ is a mobile station, $2$ is a handheld and $15$ is "other", values $3..14$ are reserved. 
 
 The second byte starts with a $4$ bit \textbf{Validity} field. Bit $1000_2$ is set if the latitude/longitude is valid. Bit $0100_2$ is set if the \textbf{Altitude} data is valid. Bit $0010_2$ is set if the velocity data is valid. Velocity data includes both \textbf{Bearing} and \textbf{Speed} data. Finally, bit $0001_2$ is set if the \textbf{Radius} data is valid. If any of these validity bits are set to zero, all the corresponding GNSS data fields should be zeroed-out by the transmitter and regarded as invalid and ignored by the receiver.
 
@@ -1376,7 +1376,7 @@ The next three bits of the second byte is the numeric \textbf{Radius} field. Thi
 
 The last bit of the second byte is the most significant bit of the $9$ bit \textbf{Bearing} numeric field. This bit is combined with the third byte and contains the bearing value. This is the heading direction for the velocity data in degrees and should never contain a value greater than 359. Zero is due north and 90 is due east, \textit{etc}.
 
-The $24$ bit, two's complement \textbf{Latitude} and \textbf{Longitude} are encoded into the next six bytes. The encode values range from $+2^{23}-1$ to $-2^{23}-1$. Note that the largest negative two's complement value, $-2^{23}$ is never used.
+The $24$ bit, two's complement \textbf{Latitude} and \textbf{Longitude} are encoded into the next six bytes. The encoded values range from $+2^{23}-1$ to $-(2^{23}-1)$. Note that the largest negative two's complement value, $-2^{23}$ is never used.
 
 The \textbf{Latitude} is specified in the fourth through sixth bytes. The value is the binary fraction of $90$ degrees, where the value $0$ represents zero degrees latitude, \textit{i.e.}, the equator, and $\pm8388607$ ($\pm2^{23}-1$) represents $\pm90$ degrees, \textit{i.e.}, the poles. A positive value is north and negative is south. This results in a resolution of approximately 39 milliseconds of arc ($\sim$1.2m).